LIBRARY 


UNIVERSITY  OF  CALIFORNIA. 


Class 


dYSICAL  LABORATORY  EXPERIMENTS 


HEAT 


BY 


H.  M.  GOODWIN,  PH.D. 

ASSOCIATE  PROFESSOR  OF  PHYSICS 
MASSACHUSETTS  INSTITUTE  OF  TECHNOLOGY 


Printed  for  the  use  of  students  of  the  Massachusetts  Institute  of  Technology, 

not  published. 


SECOND  EDITION. 


BOSTON : 

GEO.  H.  ELLIS  Co.,  PRINTERS,  272  CONGRESS  STREET. 
1904, 


3STOTE8 


ON 


PHYSICAL  LABORATORY  EXPERIMENTS 


IN 


HEAT 


BY 


H.  M.  GOODWIN,  PH.D. 


ASSOCIATE  PROFESSOR  OF  PHYSICS 
MASSACHUSETTS  INSTITUTE  OF  TECHNOLOGY. 

' 

f   UNIVSRBfT 

X^4 


or 

:.   .',:.._., L__ 


Printed  for  the  use  of  students  of  the  Massachusetts  Institute  of  Technology  r 

not  published. 


SECOND  EDITION. 


BOSTON : 

GEO.  H.  ELLIS  Co.,  PRINTERS,  272  CONGRESS  STREET. 
1904. 


C 


COPYKIGHT,  1904. 

BY  H.  M.  GOODWIN. 


s; 
, 
I 


TABLE    OF    CONTENTS. 


PACK 

PREFACE   .     „ 5 

TIIERMOMETRY:  General  Discussion 7 

Mercurial  Thermometry —  Parti 14 

Mercurial  Thermometry  —  Part  II 22 

Air  Thermometry 27 

Pressure  and  Boiling  Point 37 

CALORIMETRY:  General  Discussion . 42 

Specific  Heat 55 

Latent  Heat (51 

Mechanical  Equivalent  1 67 

Mechanical  Equivalent  II.  (Continuous  Calorimeter)  ....  72 

EXPANSION 77 

APPENDIX,  Tables 78 


1 30899 


PREFACE 


The  following  notes  cover  the  experiments  in  Heat  which 
are  required  of  students  taking  the  General  Laboratory  Course 
in  Physics.  The  laboratory  work  is  performed  subsequent  to 
or  in  some  cases  concurrently  with  the  lecture  course  on 
Heat.  Little  or  no  attention  is,  therefore,  devoted  in  these 
notes  to  theory,  deduction  of  formula^  etc.,  a  knowledge  of 
which  is  presupposed.  On  the  other  hand  a  detailed  discus- 
sion is  given  of  experimental  methods,  manipulation,  sources 
of  error  and  attainable  precision, — these  matters  being  regarded 
of  paramount  importance  in  all  work  performed  in  the  physical 
laboratory  at  the  Institute. 

The  cuts  have  been  made  from  drawings  of  the  actual 
apparatus  used  in  the  laboratory,  and  the  description  of  the 
apparatus  and  procedure  is  given  in  such  detail  that  the  student 
is  expected  by  studying  his  notes  carefully  before  the  exercise 
to  be  able  to  begin  work  at  once"  on  entering  the  laboratory 
without  further  reference  to  them.  As  most  of  the  experiments 
described  require  about  two  hours — the  usual  laboratory  pe- 
riod— for  their  completion,  preparation  for  the  work  prior  to 
the  exercise  is  essential. 

Many  of  the  questions  and  problems  at  the  end  of  each 
experiment  require  a  knowledge  of  Precision  of  Measurements 
for  their  solution.  These  may  be  omitted  by  those  students 

who  have  not  had  a  course  in  that  subject. 

H.  M.  GOODWIN. 

FEBRUARY,  1904. 


THERMOMETRY 


GENERAL    DISCUSSION 

These  notes  should  be  carefully  studied  before  performing 
the  experiments  on  Mercurial  or  Air  Thermometry. 

General  Methods. —  Thermometry  is  the  art  and  science  of 
temperature  measurement.  Any  property  of  a  substance  which 
varies  in  a  well  known  manner  with  its  temperature  may  be 
made  the  basis  of  a  system  of  thermometric  measurement,  and 
we  find  extensively  used  at  the  present  time  methods  based  on 
the  following  changes  produced  in  bodies  when  heated  or 
cooled : 

a.  Change  of  volume: — gas,  mercury,  alcohol  thermometers. 

b.  Change  of  electrical  resistance: — platinum  resistance  ther- 

mometers. 

c.  Change  of  thermo-electric  force: — thermo-electric  pyrom- 

eters. 

d.  Change  of  viscosity : — effusion  or  transpiration  pyrometers. 

In  addition  to  these  methods  should  also  be  mentioned 
specific  heat  pyrometers  and  optical  pyrometers.  The  indica- 
tions of  the  latter  are  based  on  the  intensity  or  quality  of  light 
emitted  by  bodies  at  high  temperatures.  The  term  pyrometry 
is  usually  employed  when  referring  to  methods  applicable  to 
temperatures  above  300°  C. 

The  particular  property  or  method  which  is  best  adapted  to 
any  given  case  depends  of  course  upon  the  problem  in  hand  as 
well  as  upon  the  actual  temperature  to  be  measured.  Modern 
engineering  as  well  as  pure  science  demands  methods  covering 
a  range  of  temperature  from  that  of  solid  hydrogen — 257.2°  C. 
(Dewar,  1901),  only  15°  above  the  absolute  zero,  to  that  of  the 
electric  furnace,  over  2000°  C. 

Of  the  several  instruments  mentioned  above,  gas  thermome- 
ters are  applicable  over  the  widest  range  of  temperatures. 


8       NOTES  ON  PHYSICAL  LABORATORY  EXPERIMENTS 

• 

When  filled  with  hydrogen,  they  may  be  used  down  to  near  its 
point  of  liquefaction  (—252.5°  C.,  Dewar,  1901)  and  up  to  the 
highest  temperature  which  a  porcelain  bulb  will  withstand, 
about  1400°  C.  A  nitrogen  thermometer  can  be  used  at  even 
a  higher  temperature  in  a  platinum-iridium  bulb.  Hydrogen 
diffuses  through  such  bulbs  at  high  temperatures.  Gas  ther- 
mometers afford  the  most  accurate,  absolute  method  of  ther- 
mometry  which  we  possess,  but  require  considerable  skill  in 
their  manipulation  when  a  high  degree  of  accuracy  is  desired. 
Several  convenient  commercial  forms  of  less  precision  for  high 
temperature  measurements  have,  however,  been  perfected. 

Mercury  thermometers  are  far  more  convenient  for  ordinary 
use,  and  are  applicable  at  temperatures  from  — 20°  C.  to  550°  C. 
A  high  degree  of  perfection  has  now  been  attained  in  the  con- 
struction of  these  instruments,  due  in  a  large  measure  to  a 
careful  scientific  study  of  the  nature  of  the  glass  best  adapted 
to  withstand  high  temperatures  without  change.  Fused  quartz 
has  also  been  reJpently  (1903)  proposed  as  a  suitable  substance 
of  which  to  construct  thermometers.  The  utmost  precision 
attainable  with  the  best  modern  instruments  is  0.003°  from 
0°-100°,  0.1°  from  100°-200°,  and  0.5°  from  200°-550°. 
Below  the  proper  range  of  mercury  thermometers,  which  be- 
come unreliable  considerably  above  the  temperature  at  which 
mercury  freezes,  — 39°  C.,  thermometers  of  similar  construc- 
tion but  filled  with  alcohol,  or  better,  toluene,  are  often  used. 

Less  convenient,  as  they  require  complicated  electrical 
auxiliary  apparatus,  are  the  electrical  resistance  or  platinum 
thermometers,  applicable  at  all  temperatures,  from  the  very 
lowest  up  to  about  800°  C.  With  these  instruments  tempera- 
tures can  be  measured  to  0.001°  up  to  100°;  0.01°  from  100°- 
500°;  and  0.1°  from  500°-800°. 

Another  instrument  which  of  late  years  has  rapidly  and 
deservedly  come  into  very  general  use,  is  the  thermo-electric 
pyrometer,  available  at  all  temperatures  up  to  the  melting 
point  of  platinum,  about  1700°  C.  This  instrument  is  sensitive 
to  0.01°  at  400°  and  to  1°  at  1700°  C.  With  a  suitable  galvan- 
ometer it  may  be  very  conveniently  adapted  to  commercial 
work. 


THERMOMETRY  9 

It  is  to  be  especially  noted  that,  although  both  platinum 
resistance  and  thermo-electric  pyrometers  may  have  the  high 
precision  specified  above  when  used  in  conjunction  with  suit- 
able galvanometers,  the  accuracy  of  their  indications  in  absolute 
degrees  depends  fundamentally  on  the  accuracy  with  which 
the  temperature  of  the  melting  or  boiling  point  of  various  sub- 
stances such  as  naphthalene,  benzophenone,  sulphur,  gold, 
silver,  etc.,  which  are  used  for  calibrating  the  pyrometers,  is 
known.  Such  fixed  points  have  been  determined  with  the 
hydrogen  thermometer.  The  pyrometers  mentioned  are  there- 
fore essentially  secondary  instruments  depending  upon  a  cali- 
bration which  ultimately  goes  back  to  the  hydrogen  standard. 

High  temperatures  may  also  be  more  or  less  accurately 
determined  by  several  types  of  optical  pyrometers,  transpiration 
pyrometers,  specific  heat  pyrometers,  and  others. 

The  following  notes  include  a  discussion  only  of  mercurial 
and  air  thermometry  of  ordinary  precision.  They  apply  to  the 
calibration  of  mercury  thermometers  ranging  up  to  350°  C.,  and 
correspond  to  a  precision  not  greater  than  0.05°  C.  between  0° 
and  100°,  and  less  than  this  above  100°.  For  a  discussion  of 
the  various  methods  of  pyrometry  mentioned  above  the  student 
is  referred  to  the  Laboratory  Notes  on  Heat  Measurements  by 
Prof.  C.  L.  Norton,  or  to  Le  Chatelier's  and  Boudouard's 
"Mesure  des  Temperatures  elevees"  (English  translation  by 
George  K.  Burgess).  For  the  calibration  and  preparation  of 
the  highest  grade  thermometers  the  student  should  consult 
Guillaume's  standard  treatise  on  "  Thermometrie  de  Precision," 
and  the  publications  of  the  Reichsanstalt  and  of  the  'Bureau  des 
Poids  et  Mesures  International. 

Units. —  The  fundamental  scale  of  temperature  measurement 
is  based  on  Thomson's  (Lord  Kelvin's)  absolute  thermodynamic 
scale,  which  is  independent  of  the  nature  of  any  thermometric 
substance.  The  unit  of  temperature  on  this  scale  is  called  a 
degree,  and  has  been  chosen  for  convenience  to  coincide  with 
a  degree  of  the  centigrade  scale  as  defined  below.  The  abso- 
lute scale  is  very  nearly  realized  in  practice  by  either  a  con- 
stant volume  or  constant  pressure  hydrogen  thermometer,  for  the 


10  NOTES  ON  PHYSICAL  LABORATORY  EXPERIMENTS 

deviations  of  this  gas  from  the  laws  of  a  perfect  (ideal)  gas  have 
been  shown  by  Joule's  and  Thomson's  porous  plug  experiment 
to  be  so  small  that  they  are  probably  not  greater  than  the 
experimental  errors  inherent  in  the  best  thermometric  work. 

The  hydrogen  thermometer  without  correction  has  been 
adopted  by  the  International  Bureau  as  the  practical,  ultimate 
standard  of  thermometric  measurement,  and  represents  at  the 
present  time  the  absolute  scale  of  temperature  as  nearly  as  it  is 
known.  Measurements  of  temperature  by  other  instruments 
than  the  hydrogen  thermometer,  not  excepting  even  air  or 
nitrogen  thermometers,  should  therefore,  if  their  accuracy 
warrants,  be  reduced  to  the  hydrogen  scale. 

The  Celsius  or  centigrade  scale  of  temperatures  is  that  uni- 
versally employed  in  all  scientific  work.  A  centigrade  degree 
is  T£(T  the  temperature  interval  between  the  temperature  of 
melting  ice  under  760  mm.  pressure  and  the  boiling  point  of 
pure  water  at  the  same  pressure,  these  two  fixed  points  being 
denoted  by  0°  and  100°,  respectively.  The  value  of  a  degree 
on  the  absolute  scale  and  on  the  centigrade  scale  is,  as  stated 
above,  the  same.  The  zero  of  the  former  is,  however,  273° 
below  that  of  the  latter.  The  relation  between  the  two  scales  is 
T  =  t  +  273,  where  T  and  t  are  expressed  in  absolute  and  centi- 
grade degrees  respectively,  and  273  =  o.o uWr,  the  reciprocal  of 
the  coefficient  of  expansion  of  hydrogen  gas  at  constant  pressure. 

The  Fahrenheit  scale,  still  employed  (unfortunately)  in 
much  engineering  work,  is  so  graduated  that  the  temperature 
of  melting  ice  under  standard  conditions  falls  at  32°,  and  the 
temperature  of  boiling  water  under  standard  conditions  at 
212°.  One  Fahrenheit  degree  is,  therefore,  Ti?r  of  this  tem- 
perature interval,  from  which  it  follows  that  one  degree  Fahren- 
heit equals  f  of  a  degree  centigrade. 

Any  temperature  on  the  Fahrenheit  scale  is  reduced  to  cen- 
tigrade degrees  by  the  expression 

t°C  =  ^(t'°  F  —  32°), 
or  conversely 


THERMOMETRY 


11 


On  the  Continent  the  Reaumur  scale  is  often  employed  in 
daily  life  but  never  for  scientific  work.  On  this  scale  the 
temperature  of  melting  ice  is  taken  as  0°,  and  of  boiling  water 
under  standard  conditions  as  80°.  Hence  one  degree  Reaumur 
is  equal  to  f  degrees  centigrade. 

Mercurial  Thermometers.  —  The  best  type  of  mercurial  ther- 
mometer for  general  scientific  work  is  one  with  a  cylindrical 
bulb  of  about  the  diameter  of  the  stem  and  with  the  graduations 
etched  directly  on  the  glass  (a,  figure  1).  The  graduations 
should  be  equidistant  and  should  represent  as  nearly  as  may 
be,  degrees  or  some  simple  fraction  thereof.  The  capillary 
should  terminate  in  a  small  bulb  at  the  top  to  facilitate  separat- 
ing a  thread  for  calibration  purposes,  and  also  to  prevent  acci- 
dent in  case  of  over-heating.  When  the  total 
range  of  the  thermometer  is  limited  to  a  few  de- 
grees, and  it  is  desired  to  use  it  at  widely  different 
temperatures,  as,  for  example,  in  boiling  or  freez- 
ing point  determinations,  the  capillary  is  provided 
with  a  cistern  at  the  top  as  shown  in  b,  figure  1, 
by  means  of  which  the  amount  of  mercury  in  the 
bulb  can  be  adjusted  and  the  thermometer  made 
to  read  at  any  temperature.  In  certain  casea 
when  the  thermometer  is  to  be  used  only  over  a 
limited  number  of  degrees  at  two  different  tem- 
peratures, as,  for  example,  in  calorimetric  work  in 
the  neighborhood  of  0°  and  at  room  temperature, 
the  unused  interval,  (5°-15°),  is  removed  by 
blowing  a  small  bulb  of  proper  volume  in  the 
capillary  just  above  the  5°  division  (c,  figure  1). 
This  device  avoids  making  such  sensitive  calorim- 
eter thermometers  of  excessive  length.  In  many 
thermometers  of  German  make,  the  stem  of  the 
thermometer  is  a  small  capillary  tube,  back  of 
which  is  placed  a  white  porcelain,  graduated  scale  and  the 
whole  inclosed  in  a  protecting  glass  tube  (d,  figure  1).  These 
thermometers  are  easy  to  read  and  are  convenient  for  many 
purposes,  but  the  scale  is  liable  to  move,  the  thermometers  are 


Fi 


12      NOTES  ON  PHYSICAL  LABORATORY  EXPERIMENTS 

bulky,  and  for  anything  except  relative  measurements  are  less 
desirable  than  those  described  above. 

Sources  of  Error.  —  The  temperature  indicated  by  a  mercurial 
thermometer  is  subject  to  the  following  sources  of  error,  which 
must  always  be  investigated  and  corrected  for  in  thermornetry 
of  even  moderate  precision,  i.e.,  where  an  accuracy  of  0.1°  C. 
or  more  is  desired. 

First. — Errors  arising  from  irregularities  in  the  diameter  of 
the  bore.  The  correction  for  this  source  of  error  is  known  as 
the  "calibration  correction." 

Second. — Errors  arising  from  the  fact  that  often  a  portion 
of  the  stem  of  the  thermometer  is  exposed  to  a  different  tem- 
perature from  that  of  the  bulb.  The  thermometer  will,  there- 
fore, read  too  low  or  too  high,  according  as  the  bulb  is  above  or 
below  the  temperature  of  the  stem.  The  correction  for  this 
error  is  known  as  the  "stem  exposure  correction." 

Third. — The  error  resulting  from  the  so-called  "lag"  of  the 
thermometer..  The  correction  is  referred  to  as  the  "lag  ice 
reading."  This  often  serious  source  of  error  requires  further 
explanation.  It  arises  from  the  fact  that  glass,  after  under- 
going a  sudden  change  of  temperature,  does  not  return  imme- 
diately to  its  original  volume  when  its  initial  temperature  is 
re-established,  but  lags  behind.  Thus,  if  a  thermometer  has 
been  heated  to  say  100°,  and  is  then  suddenly  cooled  to  0°,  the 
volume  of  the  bulb  will  remain  temporarily  too  large  and  the 
ice  reading  will  be  too  low.  In  the  course  of  time  the  "zero" 
will  gradually  rise  as  the  bulb  contracts  and  returns  to  its 
original  volume.  The  converse  will  of  course  be  true  if  the 
bulb  is  strongly  cooled  and  the  temperature  then  raised. 

The  amount  of  "lag"  depends  on  the  composition  of  the  glass, 
on  the  duration  of  heating  or  cooling,  on  the  temperature  to 
which  the  thermometer  is  heated,  and  on  the  rapidity  with 
which  it  is  cooled  from  this  temperature  to  zero  degrees.  On 
rapid  cooling  (e.g.,  in  one  or  two  minutes)  from  100°  to  0°,  ther- 
mometers often  show  a  lag  from  0.1°  to  0.5°,  according  to  the 
kind  of  glass  of  which  they  are  made.  The  time  required  for 
the  lag  of  a  thermometer  to  disappear,  rapidly  diminishes  the 


THERMOMETRY  13 

higher  the  temperature.  Thus  the  lag  resulting  from  a  sudden 
cooling  of  100°  would  be  several  months  in  disappearing  at 
0°  C.;  a  few  days  at  100°  C.,  and  only  a  few  hours  at  200°  C. 
It  is  evident, .  therefore,  that  the  lag  observed  in  any  case  de- 
pends to  some  extent  on  the  previous  history  of  the  ther- 
mometer as  well  as  upon  the  immediate  change  of  temperature. 

As  the  bulb  of  a  thermometer  is  necessarily  very  strongly 
heated  during  the  process  of  construction  and  filling,  the  zero 
point  of  a  new  thermometer  is  often  observed  to  rise  con- 
tinually, sometimes  by  several  degrees.  This  change  in  the 
volume  of  the  bulb  is  known  as  "ageing"  of  the  thermometer. 
It  may  often  be  removed  and  always  reduced  in  amount  by  a 
process  of  annealing,  i.e.,  heating  the  thermometer  for  several 
days  or  hours  to  a  temperature  above  that  at  which  it  is  to  be 
used,  and  then  allowing  it  to  cool  very  slowly.  Thermometers 
treated  in  this  way  are  now  prepared  by  some  French  makers; 
they  are  marked  "recuit,"  and  are  usually  much  superior  to 
others.  The  best  thermometers  are  made  at  present  either  of 
"verre  dur"  in  France,  or  of  "Jena  Glass"  in  Germany. 

Fourth. — Errors  due  to  the  value  of  one  scale  unit  not  being 
exactly  one  degree.  This  arises  from  the  fact  that  the  ice  and 
steam  points  are  not  exactly  100  scale  units  apart. 

Fifth. — Errors  resulting  from  the  deviations  of  the  ther- 
mometer from  the  absolute  or  hydrogen  scale.  The  correction 
is  known  as  the  "reduction  to  the  hydrogen  scale." 

In  high  grade  thermometry,  i.e.,  where  an  accuracy  greater 
than  0.05°  is  desired,  corrections  are  also  sometimes  necessary 
for  the  external  pressure  on  the  bulb  of  the  thermometer  which 
may  cause  its  zero  to  vary;  the  internal  pressure  of  the  mer- 
cury column  which  varies  with  the  height  of  the  column  and 
the  inclination  of  the  thermometer;  and  for  capillarity,  which 
causes  the  indication  of  a  thermometer  to  vary  according  as 
the  mercury  meniscus  is  ascending  or  descending.  To  eliminate 
the  effect  of  internal  pressure  the  International  Bureau  recom- 
mends that  thermometers  be  read  in  a  horizontal  position. 


14      NOTES  ON  PHYSICAL  LABORATORY  EXPERIMENTS 


MERCURIAL    THERMOMETRY  —  PART    I 

CALIBRATION   AND    SCALE    UNIT   OF   A   THERMOMETER 

Object. — The  object  of  the  experiment  on  Mercurial  Ther- 
mometry  is  to  give  the  student  a  practical  working  knowledge 
of  the  proper  procedure  in  measuring  temperature  by  means  of 
a  mercurial  thermometer  with  an  accuracy  of  0.1°  C.  The 
experiment  is  divided  into  two  distinct  parts:  Part  I,  the  cali- 
bration of  the  thermometer  and  the  determination  of  the  value 
of  its  scale  unit;  and  Part  II,  the  use  of  a  thermometer  as  illus- 
trated by  the  measurement  of  a  definite  temperature — the 
boiling  point  of  some  liquid — with  particular  reference  to  the 
correction  of  all  sources  of  error  affecting  the  result  is  0.1°  C. 
or  more. 

Apparatus. —  A  thermometer  will  be  assigned  to  each  stu- 
dent, to  which  he  should  attach  a  tag  bearing  his  name.  At 
the  end  of  the  exercise  thermometers  are  to  be  returned  to  an 
instructor  for  safekeeping  until  the  next  exercise.  After 
reports  on  the  completed  experiment  (including  both  Part  I.  and 
Part  II.)  have  been  handed  in  and  accepted,  the  thermometers 
with  their  receipts  are  to  be  returned  to  an  instructor,  who 
will  credit  them  to  the  student  if  found  in  as  perfect  condi- 
tion as  when  delivered.  The  thermometers  provided  (a,  figure 
1)  are  graduated  in  centigrade  degrees,  and  have  a  range  from 
about — 12°  to +  112°  C.  The  graduations  are  equidistant 
and  etched  directly  on  the  stem.  The  end  of  the  capil- 
lary terminates  in  a  small  bulb  blown  at  the  top  of  the  ther- 
mometer. 

Parallax  correctors  in  the  form  of  brass  tubes  about  one 
centimeter  in  diameter  and  ten  centimeters  long,  and  blackened 
on  the  inside,  are  mounted  vertically  in  blocks  for  reading  the 
mercury  thread.  Parallax  may  also  be  eliminated  by  placing 
the  thermometer  on  a  mirror  and  bringing  the  eye  to  such  a 
position  that  the  end  of  the  thread  and  its  image  coincide. 
For  very  accurate  calibrations  short  focus  reading  telescopes 
are  provided. 


MERCURIAL   THERMOMETRY  15 

Procedure, —  Calibration  of  a  Thermometer.  The  calibration 
consists  in  recording  the  length  of  a  thread  of  mercury  about 
ten  degrees  long,  throughout  the  entire  length  of  the  capillary. 
Since  the  volume  of  the  thread  remains  constant,  a  change  in 
its  length  at  any  point  of  the  capillary  indicates  an  irregularity 
in  the  diameter  of  the  bore  at  that  place.  From  the  variation 
in  length  of  the  thread  throughout  the  tube,  a  complete  plot 
of  the  form  of  the  bore  can  be  deduced. 

The  first  operation  consists  in  clearing  the  capillary  of  the 
mercury  which  partially  fills  it  at  ordinary  temperatures*.  To 
do  this,  allow  the  mercury  to  run  up  into  the  small  bulb  at  the 
top  of  the  capillary  until  it  is  partially  filled.  Then,  holding 
the  thermometer  in  a  nearly  horizontal  position,  give  the  upper 
end  a  quick,  light  tap  with  a  small  block  of  soft  pine  wood. 
The  thread  will  usually  break  and  the  mercury  can  then  be 
separated  into  two  parts,  one  partially  filling  the  bulb  at  the 
top,  and  the  other  filling  the  true  thermometer  bulb,  leaving 
the  whole  length  of  the  capillary  clear.  Care  should  be  taken 
not  to  allow  the  upper  bulb  to  become  completely  filled  with 
mercury,  as  under  these  circumstances  it  is  often  difficult  to 
get  the  mercury  down  again  into  the  bulb  proper. 

The  next  step  is  to  break  off  a  thread  of  suitable  length  for 
calibration  from  the  mercury  in  the  large  bulb.  This  is  a  deli- 
cate operation,  and  an  unskilled  manipulator  is  likely  to  crack 
the  thermometer  at  the  point  where  the  stem  is  joined  to  the 
bulb.  Students  should  first  observe  an  instructor  separate  a 
thread  before  undertaking  to  do  it  themselves.  The  procedure 
is  as  follows:  Hold  the  middle  of  the  thermometer  in  the  fingers 
of  the  left  hand  and  tap  the  upper  end  sharply  with  a  small 
piece  of  soft  wood  until  a  thread  of  suitable  length  is  ejected 
from  the  bulb  into  the  capillary.  Often  several  small  threads 
of  mercury  can  be  separated  and  afterwards  joined  together  to 
the  proper  length.  Several  trials  are  usually  necessary. 

Next  carry  the  thread  to  the  upper  end  of  the  stem  by  gently 
jarring  the  thermometer  in  an  inclined  position  against  the 
fingers  or  hand  supporting  the  upper  end.  It  is  much  safer  to 
do  this  at  the  start  and  to  work  the  thread  down  rather  than 


16      NOTES  ON  PHYSICAL  LABORATORY  EXPERIMENTS 

up  the  stem  during  the  calibration;  for  there  is  little  danger  of 
the  mercury  in  the  small  bulb  at  the  top  running  out  and  join- 
ing the  thread,  whereas  with  well  boiled-out  thermometers  this 
is  very  likely  to  occur  with  the  mercury  in  the  large  bulb  if 
the  thread  is  being  worked  up  the  capillary.  The  thermometer 
should  be  handled  only  at  its  extreme  ends  during  all  of  the 
following  manipulation  in  order  to  avoid  local  heating  of  the 
capillary  which  inevitably  produces  apparent  irregularities. 
In  the  finest  work  the  thermometer  should  not  be  handled  at 
all  during  calibration,  but  manipulated  from  a  distance  and 
read  by  a  telescope. 

Starting  with  the  thread  at  the  extreme  upper  end  of  the 
thermometer,  read  the  position  of  its  upper  and  lower  ends,  «j 
and  «2,  respectively,  to  0.1°  (a  good  observer  can  estimate  to 
0.05°).  Record  the  observations  in  two  vertical  columns,  leav- 
ing room  for  a  third  column  for  the  values  a-^-a^  etc.  Next 
jar  the  thread  slightly  so  that  it  moves  down  the  capillary  a 
few  tenths  of  a  degree  and  record  the  position  of  its  ends  again, 
of  i,  a'2-  This  second  observation  serves  simply  as  a  check  on 
the  first,  for  if  the  observations  have  been  made  with  care  the 
lengths  0,^-0%  and  a\-af2  should  agree,  for  it  is  quite  improb- 
able that  the  diameter  of  the  capillary  changes  by  an  appre- 
ciable amount  in  the  length  of  a  fraction  of  a  degree. 

Next  move  the  thread  about  one-half  its  length  down  the 
stem  and  record  the  position  of  both  ends,  checking  these  ob- 
servations as  before  by  a  second  observation  with  the  thread 
a  fraction  of  a  degree  further  on  in  the  capillary.  It  is  un- 
desirable that  the  end  of  the  thread  should  fall  under  a  gradu- 
ation, as  the  accuracy  of  estimation  is  less  in  this  position  than 
in  any  other,  on  account  of  the  width  of  the  graduations. 
Proceed  in  this  manner  throughout  the  whole  length  of  the 
capillary  to  below  the  zero  graduation.  Compute  all  the 
differences,  a^-a^  etc.,  before  joining  the  thread  with  the 
mercury  in  the  bulb.  If  any  large  irregularities  are  found, 
carry  the  thread  back  to  that  part  of  the  capillary  and  explore 
by  intervals  of  say  one  or  two  degrees,  instead  of  half  the 
length  of  the  thread,  in  order  to  locate  exactly  where  the  ir- 
regularity occurs. 


MERCURIAL    THERMOMETRY 


17 


The  mercury  in  the  top  of  the  thermometer  can  usually  be 
readily  rejoined  with  that  in  the  bulb  by  attaching  a  short, 
stout  string  through  the  small  loop  in  the  end  of  the  ther- 
mometer and  swinging  the  thermometer  in  a  circle.  The 
centrifugal  force  expels  the  mercury.  This  procedure  is 
always  effective,  provided  the  upper  bulb  is  not  completely 
filled  with  mercury.  If  this  is  the  case,  it  is  often  difficult  to 
connect  the  mercury,  as  a  minute  quantity  of  air  in  the  capil- 
lary will  prevent  a  thread  run  up  from  the  bulb  from,  joining 
the  mercury  at  the  top.  The  mercury  can  sometimes  be  made  to 
flow  down  into  the  bulb  by  jarring  the  thermometer,  but  more 
frequently  it  is  necessary  to  expel  a  portion  of  it  from  the  small 
bulb  by  heating  the  upper  end  of  the  thermometer  above  a 
flame.  If  the  bulb  can  be  thus  partially  emptied  of  its  mercury 
contents  and  the  remaining  mercury  allowed  to  contract  in  ice, 
this  portion  can  then  be  ejected  by  whirling  the  thermometer 
as  described  above. 

Determination  of  the  Scale  Unit. — To  determine  the  value 
of  this  quantity  the  reading  of  the  thermometer  in  steam,  fol- 
lowed by  its  reading  in  ice,  must  be  known. 

First.  Steam  Reading. — The  apparatus 
for  taking  the  steam  reading  is  shown 
in  figure  2.  The  thermometer  is  sus- 
pended by  means  of  a  section  of  a  rub- 
ber stopper  fitting  it  tightly  several  de- 
grees above  the  100°  mark,  which  rests 
upon  a  perforated  stopper  closing  the 
top  of  the  heater.  The  whole  thermom- 
eter should  hang  in  the  inner  steam 
jacket  of  the  boiler  as  shown,  the  bulb 
being  an  inch  or  two  above  the  surface 
of  the  boiling  water.  The  bulb  should 
not  be  immersed  in  the  boiling  water 
itself  for  the  following  reason:  If  the 
water  contains  impurities,  its  boiling 
point  is  slightly  raised,  which  would  of 
course  cause  the  "steam  reading"  to  be 


18      NOTES  ON  PHYSICAL  LABORATORY  EXPERIMENTS 

too  high.  If,  on  the  other  hand,  the  bulb  comes  in  contact  only 
with  the  vapor  rising  from  the  water,  the  vapor  condenses  on 
the  thermometer  and  forms  a  coating  of  pure  water  on  the 
bulb,  the  temperature  of  which  does  not  rise  above  the  true 
boiling  point  of  the  pure  water.  The  water  should  boil  briskly, 
but  not  so  violently  as  to  spatter  upon  the  bulb.  Clean  tap 
water  may  be  used,  although  distilled  water  is  preferable. 

When  the  water  has  boiled  for  five  minutes  or  more,  raise  the 
thermometer  just  high  enough  to  read  the  mercury  column, 
and  record  the  temperature.  Record  the  steam  reading  again 
several  times  and  take  the  mean  as  the  best  representative 
value.  The  thermometer  should  then  be  carefully  removed 
from  the  heater  and  allowed  to  cool  in  the  air  to  about  40°  C., 
when  it  should  be  plunged  into  the  ice  bath*  and  the  "lag  ice 
reading"  taken.  The  reading  of  the  barometer  should  also  be 
recorded,  from  which  the  true  temperature  of  the  steam  may 
be  found  in  the  steam  tables. 

Second.  The  Lag  Ice  Reading. — While  the  water  is  com- 
ing to  a  boil  in  the  preceding  operation,  prepare  a  can,  of  a 
liter  or  more  capacity,  full  of  very  finely  crushed  ice.  The  ice 
should  be  crushed  especially  fine  if  it  has  been  artificially  pre- 
pared or  the  weather  is  very  cold,  as  under  these  circumstances 
its  temperature  is  likely  to  be  considerably  below  zero.  The 
ice  must  be  clean  and  pure.  Add  enough  ice  water  to  nearly 
fill  the  can.  The  upper  layer  of  ice  should  look  white.  For 
work  to  0.1°  C.,  tap  water  may  be  used.  For  exact  work  dis- 
tilled water  must  be  used.  The  bulb  of  the  thermometer  must 
be  clean;  the  presence  on  it  of  any  impurities  soluble  in  water 
may  lower  the  temperature  in  its  immediate  surroundings  very 
appreciably.  Make  an  opening  in  the  ice  for  inserting  the 
thermometer,  with  a  clean  glass  rod. 

When  the  temperature  of  the  thermometer  has  fallen  to 
40°  C.,  plunge  the  thermometer  into  the  ice  bath  fully  to  the 
zero  mark,  and  record  readings,  every  half  minute  for  five 
minutes  or  more.  The  lowest  reading  is  to  be  taken  as  the 
"lag  ice  reading."  With  thermometers  reading  to  only  0.1°, 
the  "lag"  reading  does  not  usually  change  appreciably  during 


MERCURIAL    THERMOMETRY  19 

the  first  ten  minutes  or  so  that  the  thermometer  is  in  ice. 
With  more  sensitive  calorimeter  thermometers  the  immediate 
rise  of  the  zero  is  very  evident. 

This  completes  all  data  necessary  for  computing  the  scale 
unit. 

Computation.  —  The  computation  of  this  experiment  consists 
first,  in  the  calculation  of  the  calibration  corrections  of  the 
thermometer  and  the  construction  of  a  plot  of  corrections,  and 
second,  in  the  calculation  of  the  value  of  the  scale  unit. 

First.  Calibration  Corrections. — Construct  a  plot  with 
values  of  the  length  of  the  calibrating  thread  a-^-a^  a\-a'2,  etc., 
as  ordinates  and  corresponding  values  of  the  position  of  the 
lower  end  of  the  thread  a2,  a'2  etc.,  as  abscissae.  The  scale  of 
ordinates  should  be  such  that  the  precis  on  of  plotting  will  not 
be  greater  than  ten  times  that  of  the  data.  For  abscissa,  a  scale 
of  I"  =  10°  is  suggested.  The  best  representative  line  should  be 
a  smooth  curve  passing  among  the  points,  and  not  a  broken 
line.  This  curve  will  give  a  graphic  representation  of  the 
irregularities  of  the  capillary.  The  ordinate  corresponding  to 
any  abscissa  is  the  length  which  the  calibrating  thread  would 
have  had  in  the  capillary  if  its  lower  end  had  been  placed  at 
the  position  corresponding  to  the  abscissa  in  question.  It  is 
now  desired  to  ascertain  what  any  given  reading  of  the  ther- 
mometer would  have  been  if  the  bore  had  been  uniform 
throughout  instead  of  irregular;  in  other  words,  what  cor- 
rections must  be  applied  to  any  observed  reading  in  order  to 
reduce  it  to  the  true  reading  of  a  perfect  thermometer  of  uni- 
form bore. 

To  determine  this  we  first  proceed  to  determine  a  series  of 
consecutive  "equal  volume  points"  corresponding  to  the 
volume  of  the  mercury  thread  chosen  for  calibration.  Sup- 
pose we  start  with  the  lower  end  of  the  thread  at  any  position 
A,  near  the  lower  end  of  the  bore;  its  length  in  that 
position  will  be  given  by  the  ordinate  y1  of  the  calibration 
curve  corresponding  to  the  abscissa  A.  Its  upper  end  will 
therefore  read  A  -\-  y^  If  this  thread  be  now  supposed 
moved  along  the  tube  until  its  lower  end  stands  at  A  -\-  ylf  its: 


20     NOTES  ON  PHYSICAL  LABORATORY  EXPERIMENTS 

length  will  then  be  the  value  of  the  ordinate  y%,  corresponding 
to  the  abscissa  A  +  y1  of  the  curve,  and  its  upper  end  will 
therefore  read  A  +  y\  +  2/2.  In  this  way  we  can  determine 
the  readings  A,  A  +  1/1,  A  +  yl  +  y2,  etc.,  of  a  series  of 
points  which  mark  off,  consecutively,  equal  .volumes  along  the 
tube.  If  the  capillary  were  perfectly  uniform,  these  points 
would  be  equally  spaced.  Make  a  four  column  table.  Record 
in  the  first  column  the  reading  A,  which  in  this  case  should 
be  taken  a  few  degrees  below  zero.  The  zero  itself  is  often 
a  convenient  starting  point  if  no  temperatures  below  zero 
are  to  be  corrected  for  calibration.  Record  in  column  II  the 
ordinate  yl  corresponding  to  A  as  read  off  to  hundredths  of  a 
degree  from  the  plot.  Note  that  rejection,  in  the  computation, 
of  figures  in  the  hundredths  place  may  result  in  an  accumu- 
lated error  of  one  or  more  tenths  of  a  degree.  Record  in  this 
way  a  series  of  equal  volume  points  to  above  the  100°  division. 
Let  the  last  equal  volume  point  nearest  to  and  just  above 
100°  be  J5,  and  suppose  there  are  n  equal  volume  intervals 
between  A  and  B.  The  average  length  of  the  thread  y.m 

between  the  points  A  and  B  will  then  be  yIH  =  - 

m 

L  II.  III.  IV. 

A  yi  A  A  -  A  =  Q 

A  +  yi  y-i  A  +  y,n  A  +  ym  —  (A  +  yi) 

A  +  yi  +  2/2  y»  A  +  2y,«  A  +  2yjn  —  (A  +  yl  +  y2) 


A  +  yi  +  .  .  .  +  yn  =  B  A  +  nym  =  li  />'  —  B  —  0 

If,  therefore,  the  capillary  had  been  uniform  in  cross  section 
throughout,  and  we  had  started  with  a  thread  of  the  length 
y,H  with  its  lower  end  at  A,  the  equal  volume  points  between 
A  and  B  would  have  been  A,  A  +  ym,  A  +  2?//w,  etc.,  the 
last  point  falling  at  A  +  nyin  =•  B.  Record  these  values  in 
column  III.  The  difference  between  the  actual  equal  volume 
points,  column  I,  and  the  calculated  equal  volume  points  for  a 
perfect  thermometer,  column  III,  is  due  to  the  irregularities  in 


MERCURIAL   THERMOMETRY  21 

the  bore,  and  represents  the  corrections  which  must  be  added 
to  the  actual  readings  in  order  to  reduce  them  to  the  true 
readings  of  a  perfect  thermometer.  These  corrections  are  to 
be  recorded  in  column  IV.  The  correction  for  any  inter- 
mediate reading  on  the  thermometer  may  be  obtained  by  inter- 
polation on  a  plot  of  corrections,  which  should  be  constructed 
with  values  in  columns  I  and  IV  as  abscissae  and  ordinates, 
respectively.  This  curve  may  conveniently  be  drawn  on  the 
same  sheet  with  the  calibration  plot. 

Note  that  the  numerical  value  of  the  corrections  depends  on 
the  points  which  are  selected  for  A  and  B,  as  their  value  de- 
termines the  cross  section  of  the  imaginary  uniform  tube  to 
which  the  corrections  are  referred.  This  makes  no  difference, 
however,  in  the  value  of  the  final  reduced  temperature,  as  this 
latter  further  involves  the  value  of  the  scale  unit  (see  next 
paragraph),  which  depends  upon  the  ice  and  the  steam  reading, 
corrected  for  calibration  from  this  same  plot,  and  which  varies, 
therefore,  in  a  corresponding  manner. 

Second.  —  Value  of  the  Scale  Unit. 

Let  t's  =  mean  steam   reading   corrected   for   calibration 

by  preceding  plot, 

t'i  =  lag  ice  reading  corrected  for  calibration, 
t°   =  actual  temperature  of  steam  at  time  steam  read- 
ing was  observed. 

Then  the  mean  value  of  one  scale  unit  of  the  thermometer 
in  degrees  is 

1° 


The  value  of  t°  may  be  computed  from  the  -formula 

t  =±  100°  +  /o  (H  —  760) 

where  H  is  the  reduced  barometric  reading  in  millimeters. 
The  value  may  also  be  found  by  interpolation  from  suitable 
tables.  (See  Appendix  or  Landolt  and  Bornstein,  Physikalisch- 
Chemische  Tabellen,  p.  60). 


22  NOTES    ON    PHYSICAL   LABORATORY    EXPERIMENTS 


MERCURIAL   THERMOMETRY  — PART    II 

USE   OF   A    MERCURIAL   THERMOMETER    AND    DETERMINATION 
OF   THE    BOILING   POINT   OF   A   LIQUID 

Methods  of  Using  a  Thermometer. —  In  order  to  obtain  the 
true  temperature  corresponding  to  any  observed  reading  of  a 
mercury  thermometer,  it  is  necessary  that  a  definite  procedure 
be  followed  in  the  manipulation,  and  that  the  several  errors 
affecting  the  indications  of  the  thermometer  be  corrected 
for  in  a  definite  sequence.  There  are  two  methods  of  using  a 
thermometer  which  depend  primarily  on  the  determination  of 
its  zero  or  ice  reading,  which,  as  has  been  pointed  out,  is  a  con- 
stantly varying  quantity.  These  methods  will  be  referred  to 
as  the  "ordinary"  and  "lag  methods,"  respectively. 

The  Ordinary  Method. —  In  the  ordinary  method  the  ice 
reading  is  taken  immediately  before  the  temperature  which  is 
to  be  determined;  it  also  precedes  the  steam  reading  in  the 
determination  of  the  scale  unit,  p.  21.  Little  or  no  attention 
is  paid  to  the  lag  except  by  expert  observers.  In  other  re- 
spects this  method  is  the  same  as  the  lag  method.  It  is  liable 
to  errors  of  0.1°  C.  to  0.°5  C.  between  0°  and  100°,  and  is  there- 
fore not  to  be  followed  in  accurate  work. 

The  Lag  Method. —  In  this  method,  which  is  the  only  one  by 
which  the  full  accuracy  of  which  a  thermometer  is  capable 
can  be  attained,  the  ice  reading  is  taken  in  every  case  immedi- 
ately after  the  temperature  measurement.  The  "lag  reading," 
i.e.,  the  lowest  temperature  observed  \vhen  the  thermometer  is 
cooled  rapidly  from  the  observed  temperature  to  zero  degrees, 
is  taken  as  the  ice  reading.  It  is  sometimes  called  the  "maxi- 
mum depressed  zero,"  or  "depressed  zero."  For  work  accurate 
to  0.1°  C.  to  0.2°  C.,  the  lag  reading  may  be  taken  some  time 
before  or  after  the  actual  temperature  measurement  itself,  by 
heating  the  thermometer  to  about  this  temperature  and  cooling 
rapidly  to  zero.  The  elapsed  time  must  not,  however,  be  so 
great  that  the  zero,  meanwhile,  may  have  changed  by  more 
than  the  experimental  error.  The  law  expressing  the  relations 


MERCURIAL    THERMOMETRY  23 

between  the  lag  at  0°,  and  the  temperature  interval  through 
which  the  instrument  has  been  cooled,  will  be  found  in  Guil- 
laume's  Thermometrie. 

Stem  Exposure. —  One  other  precaution  must  always  be  ob- 
served in  temperature  measurement  whenever  the  whole  ther- 
mometer, or  at  least  the  whole  mercury  thread,  is  not  exposed 
to  the  same  temperature  as  the  bulb.  For  if  the  bulb  is  above 
the  temperature  of  the  major  portion  of  the  mercury  thread  in 
the  stem  the  thermometer  will  evidently  read  too  low,  and  con- 
versely. The  correction  is  known  as  the  stem  exposure 
correction,  and  can  be  computed  approximately  if  the 
number  of  degrees  of  mercury  in  the  exposed  stem  and 
its  temperature  is  known.  The  latter  is  determined  by 
surrounding  the  exposed  part  of  the  thermometer  with 
a  water  jacket,  the  temperature  of  which  is  determined 
by  an  auxiliary  thermometer.  A  convenient  arrange- 
ment for  this  purpose  is  a  glass  tube  closed  at  the 
bottom  by  a  perforated  rubber  stopper  through  which 
the  thermometer  passes,  as  shown  in  figure  3. 
The  stem  exposure  correction  is  computed  as  follows : 

Let  t'  =  observed   apparent  temperature    of    bulb 

corrected  for  calibration, 
ta  —  temperature  of  the  stem  as  determined  by 

auxiliary  thermometer, 

n  =  number   of  degrees  exposed  at   tempera- 
ture ta, 

0.000156  —  coefficient  of  apparent  expansion  of  mer- 
cury in  glass, 

tb  =  true  temperature  of  bulb  (desired). 
Then  the  reading  of  the  thermometer  corrected  for 
stem  exposure  will  be 

FI*  3  t"  =  tf  +  0.000156  (tb  —  ta)  n. 

As  tb  is  really  unknown  we  use  its  approximate  value  t'  with- 
out appreciable  error,  and  write 

//'  =  t'  +  0.000156  (If  —  ta)  n. 


24     NOTES  ON  PHYSICAL  LABORATORY  EXPERIMENTS 

It  is  easy  to  see  that  at  100°  the  correction  may  amount  to 
1°  C.  It  is  a  source  of  error  too  often  neglected  in  work  of 
even  moderate  precision. 

Order  of  Application  of  Corrections.  —  Suppose  that  the  ther- 
mometer used  has  been  calibrated  and  a  plot  of  corrections 
determined,  and  that  the  value  of  its  scale  unit  is  known.  A 
temperature  is  subsequently  determined  as  described  above, 
the  proper  data  for  the  exposed  stem  correction,  as  well  as  the 
lag  ice  reading,  being  observed.  The  true  temperature  corre- 
sponding to  such  data  is  then  computed  as  follows,  the  correc- 
tions being  applied  in  the  order  indicated : — 

Let  t  =  observed  temperature  of  the  thermometer, 
ta  =  observed  temperature  of  exposed  stem, 
n  =  number  of  degrees  exposed  at  temperature  ta, 
ti  —  lag  ice  reading, 
a  =  value  of  one  scale  unit. 

First. — Calibration  Correction.  Correct  the  observed  tem- 
perature for  calibration  by  means  of  the  plot  of  calibration 
corrections.  The  correction  taken  with  its  proper  sign  should 
always  be  added. 

f  =  t  +  c. 

Second. — Stem  Exposure  Correction. 

f  =  tf  +  0.000156  (tf  —  ta)  n. 

Third. — Lag  Ice  Reading. 

i>»  --  f  _  t. . 

Fourth. — Reduction  to  Degrees  by  Value  of  Scale  Unit. 

t"  =i  a  t'". 

Fifth. — Reduction  to  Hydrogen  Scale.  This  last  correction 
may  be  omitted,  although  if  the  kind  of  glass  of  which  the  ther- 
mometer is  constructed  is  known,  the  correction  may  be  readily 
obtained.  To  determine  the  correction  experimentally  a  direct 
comparison  of  the  mercury  and  hydrogen  thermometer  would 
be  necessary. 

The  amount  of  this  correction  for  various  kinds  of  glass  is 
given  in  the  following  table,  taken  from  Guillaume's  Ther- 
mometrie : — 


MERCURIAL   THERMOMETRY 


25 


ALGEBRAIC  EXCESS  OF  READING  ON  SCALE  SPECIFIED  OVER  THAT  OF  THE  HYDRO- 
GEN THERMOMETER. 


Scale.              10° 

20° 

30° 

40° 

50° 

60° 

70° 

80° 

90° 

Nitrogen  .    .    .    +0006 

+0.010 

+0011 

+0.010 

+0.009 

+0.005 

+0.001 

—0.002 

—0.003 

Verre  dur     .    .  ;  +0.052  j  +0.085 

+0.102 

+0.107 

+0.103 

+0.090    +0.072 

+0.050 

+0.026 

French  crystal 

(hard)     ...    +0.064 

+0.107 

+0.130 

+0.138 

+0.134 

+0.119 

+0.097 

+0.069 

+0.036 

French  crystal  j 

(ordinary)  .    .    +0.067 

+0.112 

+0.137 

+0.147 

+0.144 

+0.130 

+0.107 

+0.076 

+0.041 

Jena  glass  16™    +0.057 

+0.093 

+0.113 

+0.119 

+0.116 

+0.102 

+0.083 

+0.058 

+0.031 

Jena  glass  S9™    +0.024 

+0.036 

+0.037 

+0.033 

+0.026 

+0.016 

+0.007 

+0.001 

—0.002 

English  crystal 

(Wiebe)  .    .    .  j     o.ooo 

+0.02 

+0.03 

0.00 

—0.03 

Fig.  4. 


Object.— The  object  of  the 
following  experiment  is  to 
give  practice  in  the  proper 
method  to  follow  in  exact 
mercurial  thermometry.  The 
procedure  is  illustrated  by 
the  determination  of  the 
boiling  point  of  some  liquid. 

Apparatus. —  The  student 
is  to  use  the  thermometer 
which  he  has  calibrated. 
The  apparatus  required  is 
shown  in  figure  4.  A  is  a 
small  boiling  flask  provided 
with  a  side  tube  B,  which 
is  connected  with  a  return 
condenser  C.  The  flask  is 
clamped  in  position  on  an 
asbestos  and  wire  gauze  sup- 
port, so  constructed  that  the 
direct  flame  does  not  come 
in  contact  with  the  flask. 
The  thermometer  is  held  in 
place  by  a  cork  fitting  the 
neck  of  the  flask;  the  bulb 


26      NOTES  ON  PHYSICAL  LABORATORY  EXPERIMENTS 

should  be  wholly  immersed  in  the  liquid.  The  addition  of  glass 
beads,  garnets,  or  scraps  of  platinum  to  the  flask  is  frequently 
necessary  to  insure  quiescent  boiling.  The  exposed  stem  of  the 
thermometer  is  provided  with  a  stem  exposure  tube  filled  with 
water,  the  temperature  of  which  is  determined  by  an  auxiliary 
"General  Use"  thermometer.  The  student  will  be  given  a 
liquid  whose  boiling  point  is  to  be  determined. 

Procedure. — First.  The  flask  should  be  about  one-half 
filled  with  the  liquid  to  be  investigated.  'Arrange  the  stem 
exposure  tube  and  thermometer  as  shown  in  the  figure.  Bring 
the  liquid  to  brisk  but  not  violent  boiling.  The  vapor  should 
be  completely  condensed  in  the  condenser;  if  this  is  not  the 
case  the  boiling  point  of  a  solution  will  not  be  constant,  but 
will  continually  rise  owing  to  the  gradual  increase  in  its  con- 
centration. Allow  the  liquid  to  boil  for  five  minutes  or  more, 
during  which  time  prepare  an  ice  bath  for  the  determination  of 
the  lag  ice  reading.  At  the  end  of  five  minutes  record  four  or 
five  readings  of  the  thermometer  and  take  their  mean.  Record 
also  the  temperature  ta  of  the  water  surrounding  the  exposed 
stem  as  indicated  by  the  auxiliary  thermometer,  and  also  the 
number  of  degrees  of  mercury  thread  exposed  at  this  temper- 
ature. The  reading  of  the  barometer  and  its  attached  ther- 
mometer should  also  be  recorded. 

Second.  Turn  out  the  gas,  remove  the  thermometer  from 
the  flask  and  allow  it  to  cool  in  the  air  to  about  40°.  Then  de- 
termine the  lag  ice  reading  as  already  described  on  p.  18. 

Computation. —  Compute  the  true  boiling  point  of  the  given 
liquid,  stating  the  reduced  barometric  pressure  at  the  time  of 
the  experiment. 

Problems. — 1.  How  many  degrees  of  a  thermometer 
may  be  exposed  at  a  temperature  of  20°  C.  with  its  bulb  at 
100°  C.,  and  the  stem  exposure  correction  be  less  than  0.1°  C.? 

2.  What  will  be  the  error  resulting  from  neglecting  the 
stem  exposure  correction  of  a  thermometer  reading  300°  C. 
with  200°  of  the  stem  exposed  at  temperature  of  20°  C.  ? 


AIR    THERMOMETRY 


27 


AIR   THERMOMETRY 

Object. —  This  experiment  illustrates  the  use  of  the  air  ther- 
mometer for  temperature  measurement  or  for  the  determina- 
tion of  the  coefficient  of  expansion  of  a  gas.  The  boiling  point 
of  water  under  atmospheric  pressure  is  to  be  determined,  assum- 
ing the  value  of  the  coefficient  of  expansion  of  the  air  in  the 
thermometer  known. 

Apparatus. —  The  apparatus  provided  is  a  constant  volume 
air  thermometer  consisting  of  a  thin  glass,  spherical  (or  cylin- 
drical) bulb  A  blown  at 
the  end  of  a  capillary 
tube  B,  which  is  bent  in 
the  manner  shown  in 
figure  5.  The  other 
end  of  the  capillary  is 
connected  to  a  glass 

T  tube  C,  about  one  centi- 

meter in  diameter  which 
is  sealed  into  a  three 
way  steel  stop-cock  S, 
by  means  of  wax.  This 
cock  is  connected  by 
heavy  rubber  pressure 
tubing  to  a  second  glass 
tube  D,  of  the  same  in- 
ternal diameter  as  C. 
Both  C  and  D  are  fixed 
to  movable  slides  which 
can  be  clamped  at  any 
desired  height  along  the 
vertical  support  H. 
The  height  of  D  may 
be  further  adjusted  by 
means  of  a  fine  adjust- 
ing screw  E.  A  scale 
Fjg  5  g  r  a  d  u  a  t  e  d  in  milli- 


28     NOTES  ON  PHYSICAL  LABORATORY  EXPERIMENTS 

meters  is  attached  to  the  front  side  of  the  support  H.  The 
height  of  the  mercury  column  in  C  and  D  is  read  on  this  scale 
by  means  of  a  cathetometer  or  reading  telescope. 

The  three  way  stop  cock  S  requires  further  explanation.  Its 
construction  will  be  seen  from  figure  6.  1  is  a  vertical  section; 
2,  a  front  view  of  the  cock  in  the  same  position  when  it  is 

closed.  It  is  seen  that  the  through 
boring  is  in  the  direction  of  the 
handle  of  the  cock,  and  the  lateral 
boring  at  right  angles  to  this  direc- 
tion. This  is  indicated  on  the  cock 
by  the  marked  or  flattened  side.  The 
only  positions  in  which  the  cock  is 

closed  is  when  the  handle  stands  at  45°,  as  hi  1,  2  and  5.  3  is 
the  proper  position  for  putting  C  and  D  into  free  communica- 
tion; 4  is  the  position  for  filling  the  thermometer  with  dry  air, 
and  for  drawing  off  the  mercury  from  C. 

The  boiler  consists  of  a  double  walled  vessel  of  copper  in 
which  the  vapor  of  the  boiling  liquid  circulates  up  around  the 
bulb  and  down  between  the  inner  and  outer  walls,  thus  pre- 
venting direct  radiation  from  the  outside  walls  on  to  the  bulb 
of  the  thermometer.  A  slotted  screen  M  protects  the  mer- 
cury columns  from  the  direct  radiation  of  the  boiler. 

Procedure. — First.  To  fill  the  thermometer  with  pure,  dry 
air.  (This  operation  may  be  omitted  if  the  instructor  states 
that  the  apparatus  is  already  properly  filled.)  Lower  the  bulb 
into  the  heater  and  bring  the  water  to  a  boil.  Lower  D  below 
the  level  of  the  mercury  in  C,  and  then  open  the  stop-cock  S, 
so  that  the  mercury  in  C  flows  back  into  D  until  the  horizon- 
tal opening  of  the  stop-cock  S  is  clear.  Connect  this  with  a 
T-tube,  one  end  of  which  is  attached  by  means  of  rubber 
tubing  to  the  drying  apparatus,  and  the  other  to  an  air  pump, 
as  in  figure  7.  Both  of  the  rubber  tubes  should  be  provided 
with  independent  pinch  cocks,  P1  and  P2.  The  drying  appa- 
ratus should  be  so  arranged  that  fresh  air  is  drawn  through  a 
strong  solution  of  caustic  potash  or  soda  lime,  to  remove  car- 
bonic acid,  then  through  several  dehydrating  agents,  such  as 


AIR    THERMOMETRY 

calcium  chloride  or  strong  sulphuric  acid,  arid  finally  over 
phosphorous  pentoxide.  While  the  water  is  boiling,  pump  the 
air  from  A  through  Px,  P2  being  closed.  Then  close  Pl  and 
gradually  open  P2,  allowing  dry  air  to  be  drawn  into  the  appa- 
ratus. Close  P2  and  open  Px.  Repeat  the  above  operation  a 

dozen  times  or  more.  After  the  last 
filling  allow  the  bulb  to  cool  to  room 
temperature  before  disconnecting  the 
drying  apparatus.  Then  turn  the  stop- 
cock S,  so  that  C  communicates  freely 
with  D,  and  raise  the  latter  until  the 
mercury  appears  in  C.  The  thermome- 
ter is  now  filled  with  dry  air  at  ap- 
Fiff  7  proximately  atmospheric  pressure  and 

room  temperature. 

Second.  To  determine  the  pressure  when  the  gas  occupies  a 
definite  reference  volume  at  a  known  temperature, — the  melting 
point  of  ice. — This  operation  in  gas  thermometry  corresponds 
to  the  determination  of  the  zero  point  of  a  mercurial  ther- 
mometer. 

Crush  enough  ice  to  fill  the  inner  cylinder  of  the  heater. 
Cover  the  wire  bottom  of  the  cylinder  with  about  an  inch  of 
ice;  then  lower  the  thermometer  bulb  into  it  until  the  capillary 
stem  rests  on  the  bottom  of  the  slot  in  the  side  of  the  heater. 
During  this  operation  be  sure  that  S  is  closed,  otherwise 
the  mercury  will  run  over  into  the  bulb.  If  this  should  occur, 
speak  to  an  instructor.  Care  must  be  taken  to  exert  no  press- 
ure on  the  bulb,  otherwise  the  thermometer  is  likely  to  snap 
off  at  C.  Pack  the  bulb  and  stem  of  the  thermometer  with 
ice,  filling  the  inner  cylinder  completely.  Cover  the  top  of  the 
ice  with  a  piece  of  felt  or  flannel  to  prevent  circulation  of  air 
currents.  Place  the  cover  on  the  heater  and  allow  the  appa- 
ratus to  stand  at  least  ten  minutes  before  taking  any  readings. 
A  thermometer  T  should,  in  the  meantime,  be  suspended  along 
the  vertical  support  H  with  its  bulb  close  to  C,  in  order  to  obtain 
the  temperature  of  the  air  and  mercury  in  C,  both  of  which  are 
assumed  to  be  at  the  same  temperature. 


30      NOTES  ON  PHYSICAL  LABORATORY  EXPERIMENTS 

While  waiting  for  the  air  to  cool  to  0°,  record  the  height  of 
the  barometer  and  its  attached  thermometer.  After  about  five 
minutes  open  the  stop-cock  S  cautiously,  so  that  C  and  D 
freely  communicate,  and  adjust  the  height  of  D  so  that  the 
mercury  in  C  just  comes  in  contact  with  the  point  of  the  black 
glass  reference  mark.  The  adjustment  should  be  made  with 
a  rising  meniscus.  If  the  mercury  column  now  remains  at  rest 
for  several  minutes  (the  cock  S  being  open),  the  air  in  the 
bulb  may  be  assumed  to  have  reached  a  constant  temperature, 
and  the  height  of  the  mercury  columns  in  C  and  D  should  be 
recorded.  This  is  to  be  done  by  means  of  a  reading  telescope 
provided  with  a  horizontal  cross  hair.  The  field  of  view  must 
include  both  the  mercury  meniscus  and  the  graduated  scale. 
Estimate  readings  to  0.1-0.05  mm.  For  very  accurate  work, 
(readings  to  0.01-0.02  mm.),  the  eyepiece  of  the  telescope 
must  be  provided  with  a  filar  micrometer,  or  a  ca  the  tome  ter 
must  be  used.  Repeat  the  adjustment  and  observations  two  or 
three  times  and  take  the  mean  of  the  readings  in  computing 
the  final  pressure.  Record  the  temperature  ^  of  the  ther- 
mometer T.  As  long  as  the  mass  of  air  in  the  bulb  remains 
unchanged,  the  reduced  pressure  poj  corresponding  to  this 
data,  will  be  the  same  whenever  the  air  is  cooled  to  0°  C.  and 
the  volume  is  adjusted  so  that  the  mercury  in  C  stands  at  the 
reference  mark.  For  a  given  thermometer  containing  a  constant 
amount  of  gas,  this  pressure  p<>  is  a  constant.  It  is  always  well, 
however,  to  determine  the  pressure  corresponding  to  the  ice 
reading  prior  to  a  temperature  determination  in  order  to  elimi- 
nate possible  errors  arising  from  leakage  or  change  of  volume 
of  the  bulb. 

Third.  To  measure  an  unknown  temperature. — To  measure 
any  temperature  with  a  given  air  thermometer  for  which  />„ 
has  been  determined  as  above,  it  is  only  necessary  to  find  the 
pressure  which  will  bring  the  gas  to  the  original  reference 
volume  when  heated  to  the  temperature  in  question.  The 
method  and  procedure  is  to  be  illustrated  by  determining  the 
boiling  point  of  water  (or  any  other  liquid  provided),  under 
atmospheric  pressure.  Close  the4  stop-cock  /S.  Light  the 


AIR   THERMOMETRY  31 

under  the  boiler,  which  should  be  filled  with  water  to  a  depth 
of  three  or  four  centimeters.  Tap  water  is  sufficiently  pure  for 
this  experiment,  although  for  work  of  extreme  accuracy,  dis- 
tilled water  should  be  used.  The  ice  need  not  be  removed  from 
the  heater  unless  it  is  desired  to  save  time,  as  the  steam  will 
quickly  cause  it  to  melt  and  run  back  into  the  boiler.  While 
waiting  for  the  ice  to  melt,  again  record  the  reading  of  the 
barometer  and  its  attached  thermometer.  When  the  ice  has 
melted  and  the  water  has  boiled  briskly  for  five  minutes,  raise 
D  about  twenty  centimeters  and  carefully  open  S.  Adjust  the 
height  of  D  until  the  mercury  in  C  comes  exactly  to  the  refer- 
ence mark.  Wait  several  minutes  to  see  if  the  pressure  remains 
constant;  if  so,  record  the  position  of  C  and  D  as  before.  Re- 
adjust two  or  three  times  and  take  the  mean  of  the  readings. 
Record  also  the  reading  t%  of  the  thermometer  T.  Finally  close 
S,  turn  off  the  gas  and  raise  the  thermometer  out  of  the 
heater. 

Fourth.  To  determine  the  stem  exposure  correction. — If  a 
portion  of  the  stem  of  a  mercurial  thermometer  is  at  a  different 
temperature  from  that  of  the  bulb,  a  stem  exposure  correction 
(p.  23)  has  been  shown  to  be  necessary.  A  similar  correction 
is  also  necessary  in  the  case  of  an  air  thermometer,  due  to  the 
fact  that  the  air  in  the  stem  and  in  C  is  not  at  the  same  tem- 
perature as  that  in  the  bulb  when  the  latter  is  placed  in  ice, 
steam,  etc.  The  amount  of  this  correction  depends  upon  the 
ratio  of  the  volume  of  air  contained  in  C  and  the  stem,  to  the 
volume  of  the  bulb.  A  comparatively  rough  determination  of 
this  ratio  suffices  to  compute  the  correction  with  sufficient 
accuracy.  The  volume  of  the  exposed  stem  is  usually  made  as 
small  as  possible,  so  that  the  resulting  correction  shall  be  small. 
The  volume  V  of  the  bulb  is  to  be  computed  from  three  measure- 
ments of  its  circumference  (or  diameter),  taken  in  planes  at  right 
angles  to  each  other.  The  circumference  may  be  measured 
with  a  tape,  or  better  by  a  strip  of  paper,  the  length  of  which 
is  afterwards  measured  on  a  scale.  In  work  of  extreme 
accuracy  the  volume  may  be  determined  by  filling  the  bulb 
with  water  or  mercury  and  weighing.  The  volume  of  the 


32      NOTES  ON  PHYSICAL  LABORATORY  EXPERIMENTS 

capillary  which  extends  into  the  heater  may  be  neglected  in 
comparison  with  the  volume  of  the  bulb. 

To  determine  the  volume  v  of  the  air  in  C  above  the  mer- 
cury, and  of  the  capillary  outside  of  the  heater,  raise  D  above 
C  and  carefully  open  S  into  position  3,  until  the  mercury  com- 
pletely fills  C  and  the  capillary,  up  to  the  point  where  it  enters 
the  heater.  Close  S  as  in  5,  figure  6.  Finally  turn  the  cock 
into  position  4  and  allow  the  mercury  to  run  out  into  a 
previously  weighed  small  beaker  until  the  meniscus  just 
reaches  the  reference  point.  From  the  weight  of  this  mercury 
the  volume  v  may  be  at  once  computed.  Weighings  to  one 
per  cent,  are  sufficiently  accurate. 

Fifth.  On  completing  the  experiment  be  sure  that  the 
apparatus  is  left  as  follows:  C  should  be  raised  so  that  the 
bulb  is  out-  of  the  heater.  The  mercury  in  C  should  stand 
two  or  three  centimeters  below  the  reference  point,  to  prevent 
its  soiling  the  inside  of  the  tube  where  the  readings  are  taken. 
The  stop-cock  S  should  be  closed,  and  D  raised  above  C,  so 
that  there  may  be  no  tendency  for  air  to  leak  into  the  appa- 
ratus at  the  cock  S. 

Computation. — The  temperature  of  the  steam  is  to  be  com- 
puted from  the  data  obtained. 

By  the  combined  laws  of  Boyle  and  Gay-Lussac  we  have 
for  a  perfect  gas,  and  practically  also  for  hydrogen,  oxygen, 
nitrogen,  and  air, 

PPt  —  PoV0  (1  +  at)         (1) 

where  a  is  the  coefficient  of  expansion  of  the  gas  and  /  is  its 
temperature  expressed  in  degrees  centigrade.  If  v0  =  rtj  we 
have,  solving  the  equation  for  /, 

t=Pt~Po  (2) 

ap0 

from  which  t  may  be  computed  at  once  when  the  pressure  p0 
at  zero  degrees,  and  the  pressure  pt  at  /°,  together  with  the  co- 
efficient of  tension  a-  (equal  practically  to  the  coefficient  of  ex- 
pansion) of  the  gas  is  known.     For  dry  air  a  —  0.003670. 
This  simple  formula  does  not  apply  exactly,  however,  to  the 


AIR   THERMOMETRY  33 

data  taken  in  the  preceding  experiment,  for  the  condition 
v0  =  rt  is  not  exactly  fulfilled;  i.e.,  the  total  mass  of  gas  is 
not  brought  to  the  same^  volume  at  0°  and  at  t°,  for  the  follow- 
ing reasons:  — 

First,  the  volume  of  the  bulb  increases  when  heated  from 
0°  to  t°,  owing  to  the  expansion  of  the  glass;  and  second,  the 
exposed  portion  of  the  air  in  C  and  in  the  capillary  does  not 
occupy  the  volume  it  would  if  it  were  brought  to  0°  and  t°, 
respectively.  It  is  necessary,  therefore,  to  obtain  correct  ex- 
pressions for  v0  and  vt  and  to  substitute  them  in  the  general 
formula  (1)  before  solving  for  t. 

Let  HI,  H%  =  the  reduced  barometer  readings  at  the  time 

of  ice  and  steam  readings,  respectively; 

hi,  /z-2  =•  the  mean  manometer  pressures  reduced  to  0°,  com- 
puted from  the  observations  taken  at  the  temperature 
of  ice  and  steam,  respectively; 
ti,  t2  =  the  temperature  of  the  mercury  columns  at  the  time 

of  taking  the  ice  and  steam  readings,  respectively; 
V  —  the  computed  volume  of    the    bulb,  which    may    be 
assumed  with  sufficient  approximation  to  be  its  volume 
atO°; 

x  —  the  volume  of  exposed  stem; 
k  =  the    mean    coefficient    of    cubical    expansion    of  glass, 

—  0.000027  per  degree  centigrade. 

The  height  hi  of  the  mercury  column  DI  —  Ci  reduced  to  0° 
is 

*  - 


1  +  0.000181*! 
—  (Di  —  Ci)  (1  —  0.000181*!)  approximately. 

Note   that   this   may   be   negative,    which   means   that    the 
pressure  of  the  gas  at  0°  is  less  than  one  atmosphere. 
Similarly 

h2  =  (D2  —  C2)  (1  —  0.000181  /2)  approximately. 

As  the  quantities  D  and  C  are  mean  results  of  observations 
taken  to  one-tenth  of  a  millimeter  they  should  be  carried  in  the 


34     NOTES  ON  PHYSICAL  LABORATORY  EXPERIMENTS 

computation  to  hundredths  of  a  millimeter.     It  will  be  seen 
that  the  reduction  to  0°  affects  only  the  last  two  places  of  sig- 
nificant figures  in  h,  hence  three  significant  figures  in  the  com- 
putation of  the  correction  term  are  sufficient. 
The  final  reduced  pressures  p0  and  pt  are 

p0  =  Hl  +  h1 

pt  =  H2  +  ^2- 

We  have  next  to  determine  the  true  volume  v0  and  vt  which 
the  air  would  have  occupied  if  it  had  all  been  at  0°  and  t°, 
respectively.  The  air  in  the  exposed  stem  of  volume  v  at  tf 

and  pressure  p0  would  have  occupied  the  volume  -i — ; —  -  at  0° 

1  -}-  ati 

and  pressure  p0.     Hence  the  total  volume  which  the  air  in  the 
thermometer  would  have  occupied  at  0°  is 

v0  =  V  + 


1  +  at,  ' 

Similarly,  a  volume  of  air  v  in  the  exposed  stem  at  t2°  and 
pressure  pt  would,  at  t°  and  under  the  same  pressure  pt,  have 

occupied  the  volume  ^    ,      -  (1  +  at). 

If  the  volume  of  the  bulb  is  taken  as  V  at  0°,  at  t°  it  will  be 
V  (1  +  kt).  Hence  the  volume  which  the  total  mass  of  air 
would  have  occupied  at  t°  and  pressure  pt  is 


Substituting  these  values  in  equation  (1)  we  have 
»  [V  (1  +  *0  +  r  i±-£J  =  p.  (V  +  T^--)  n  +  at). 

V 

Dividing  by  V  (I  +  at)  and  putting  r  =p-for  brevity  this 
equation  becomes 

l  +  kt  ,  l\  (  1 

*  r=  r 


AIR    THERMOMETRY 


35 


Solving  for  t 


apoil   + 


1  +  at 


aPt 


I  +  at2 


(apo  _  kpl) 

r 


kp, 


(3) 


If  ti  does  not  differ  much  from  t2,  so  that  without  introduc- 
ing an  error  greater  than  the  experimental  error  they  may  be 
assumed  equal,  this  formula  reduces  to 


t  = 


Pt  — 

Po 

i    i         r 

!  +  *, 

np0  —  kpt 

r              a                       . 

1  +  a/!  ap0  -  kpt  (Pt       Po) 

(4) 


The  form  of  the  correction  factor  in  brackets  can  be  further 
simplified  by  writing  it  in  the  approximate  form 


1  +  a/!   ap0  —  kpt 


If,  in  this  correction  term,  kpt  can  be  neglected  in  compari- 
son with  apQ,  the  correction  further  simplifies  to 

1  +  ,^-r^, 
1  +  a/j     p0 

and  equation  (4)  becomes 


Pt 


ap0  —  kpt 


1  + 


1  + 


(5) 


Notice  that  formula?  (4)  and  (5)  reduce  at  once  to  (2)  if  the 

7) 

stem  exposure  correction  involving  --  =  r  and  the  correction 

for  the  expansion  of  the  bulb,  kptj  are  negligible. 

Coefficient  of  Expansion  of  a  Gas. — If  instead  of  solving  for 
t,  this  is  known,  the  above  data  may  be  used  for  determin- 


36      NOTES  ON  PHYSICAL  LABORATORY  EXPERIMENTS 

ing  a,  the  coefficient  of  expansion  of  the  gas.  Inspection  of 
equation  (3)  will  show  that  the  equation  contains  a  in  three 
places  in  such  a  way  that  a  general  solution  is  exceedingly 
laborious.  Since  a  enters  only  in  small  corrections  factors 

in  the  terms  —  _  —  -   and    _     —     we    may    assume    an    ap- 
1  +  a/!  I  +  at2' 

proximate  value  for  it  in  these  terms  and  solve  for  a  in  the 
term  at.  If  the  value  thus  obtained  differs  too  widely  from 
the  assumed  value  of  a,  a  second  or  even  third  approximation 
must  be  made.  One  approximation  usually  suffices.  Solving 
for  a  in  (3)  under  this  assumption  we  obtain 


If  /!  and  #2  are  so  nearly  the  same  that  they  may  be  assumed 
equal,  this  equation  becomes 


a  = 


or  simplifying  the  correction  factor  by  an  approximation, 


1  4- «/, 

Problems. —  1.     How  precise  should  the  ratio   ~=  r  be 

determined  in  this  experiment  in  order  that  the  resulting  devi- 
ation in  t  (formula  5)  shall  not  exceed  0.3  per  cent? 

2.  What  precision  in  v  and  V  does  this  correspond  to  in 
the  actual  apparatus  used? 

3.  How  precise  should  a  (formula  5)  be  known  for  a  pre- 
cision of  0.3   per  cent  in    t,  assuming   other   sources  of  (jrror 
negligible? 


PRESSURE   AND    BOILING    POINT  37 


PRESSURE  AND  BOILING  POINT,  AND  PRESSURE 
OF  SATURATED  VAPOR 

Object. —  This  experiment  is  designed  to  study  the  change  of 
the  boiling  point  of  a  liquid  under  varying  pressure,  and  to  illus- 
trate the  dynamical  or  boiling-point  method  of  determining  the 
pressure  of  saturated  vapor  at  different  temperatures.  The  ex- 
periment also  furnishes  data  for  illustrating  the  application  of 
the  fundamental  thermodynamic  formula  for  the  liquid-vapor 
state  to  the  calculation  of  the  specific  volume  of  saturated  vapor. 

Discussion.  —  A  pure  liquid  can  exist  in  equilibrium  with  its 
vapor  at  any  definite  temperature  and  one  corresponding 
pressure,  or  conversely  at  any  definite  pressure  and  one  cor- 
responding temperature.  If  at  any  temperature  the  external 
pressure  on  a  liquid  is  greater  than  the  pressure  of  its  vapor 
and  the  temperature  of  the  liquid  be  gradually  raised,  the 
pressure  of  the  vapor  will  increase  until  it  is  exactly  equal  to 
the  external  pressure  when  the  liquid  will  begin  to  boil.  The 
pressure  at  which  a  liquid  boils  is  therefore  a  direct  measure 
of  the  pressure  of  its  saturated  vapor  at  its  boiling  point,  and 
the  determination  of  the  boiling  point  of  a  liquid  under  dif- 
ferent pressures  affords  an  excellent  method  for  the  investigation 
of  the  pressure  of  saturated  vapor  at  various  temperatures.  This 
is  known  as  the  Dynamical  Method  of  vapor  pressure  measure- 
ment as  distinct  from  the  Statical  Method,  in  which  the  liquid 
is  introduced  into  the  top  of  a  barometer  maintained  at  a  known 
temperature  and  the  depression  of  the  mercury  column  observed. 
The  Dynamical  Method  is  by  far  the  more  accurate,  as  it  is  but 
little  affected  by  slight  impurities  in  the  liquid.  The  Statical 
Method,  on  the  other  hand,  is  liable  to  grave  errors  from  this 
source,  particularly  if  the  impurities  are  very  volatile. 

The  only  rigid  relation  holding  between  the  pressure  p  and 
the  boiling  point  t  of  a  liquid,  or  in  other  words,  between  the 
temperature  t  and  the  pressure  p  of  its  saturated  vapor,  is  the 
thermodynamical  equation1 


Introduction  to  Physical  Science,"  p.  161. 


dt  _        „ 

a  see  anv  work  on  Thermodynamics,  a: 

95;  Noyes' 


i  For  deduction  of  this  formula  see  any  work  on  Thermodynamics,  as  Clausius 
"Mechanical  Theory  of  Heat,"  p.  129;  Peabody's  "Thermodynamics,"  p. 


38      NOTES  ON  PHYSICAL  LABORATORY  EXPERIMENTS 

where  r  is  the  latent  heat  of  vaporization  of  the  liquid  at  t°  C., 
T  the  absolute  temperature  corresponding  to  t°  C.,  and  v^ 
and  v2,  the  corresponding  specific  volume  of  the  liquid  and 
its  saturated  vapor,  respectively.  As  these  last  quantities  as 
well  as  r  are  functions  of  the  temperature,  the  above  equation 
cannot  be  integrated  without  making  simplifying  assumptions, 
or  by  the  aid  of  empirical  relations  between  the  quantities 
r,  Vi,  v2  and  the  temperature  t.  Thus  for  water,  Clausius  de- 
duces from  Regnault's  measurements  the  following  empirical 
formula  for  r: — 

r  =  607  —  0.70&. 

The  exact  way  in  which  t'2  varies  with  t,  i.e.,  the  form  of 
function  v2  =  /  (t)  is  known  for  only  a  few  vapors.  Sat- 
urated vapors  are  often  assumed  to  follow  Boyle's  law,  i.e., 

7?  T 
v2  = ,  but  this  assumption  is  in  most  cases  only  a  rough 

approximation  and  is  liable  to  lead  to  erroneous  results. 

Equation   (1)    is   of  great  value   in   computing   the   specific 

dj) 
volume  v2  of  saturated  vapor  when  -^-  and  r  are  known,  as  r2 

itself  can  be  experimentally  determined  with  accuracy  only 
with  great  difficulty.  The  specific  volume  i\  of  the  liquid  is 
approximately  equal  to  unity,  and  therefore  is  usually  negligible 
compared  with  vz  in  any  computation.  The  experimental 

determination  of  -5-  affords  therefore  a  valuable  means  of  find- 
ing indirectly  the  specific  volume  of  saturated  vapor. 

Equation  (1)  is  not  limited  to  changes  from  the  liquid  to  the 
vapor  state,  but  holds  equally  true  for  all  changes  of  state,  for 
example  the  melting  of  ice  to  water,  in  which  case  r  denotes 
the  latent  heat  of  fusion,  T  the  absolute  melting  point,  i\  and  ra 
the  specific  volumes  of  the  substance  in  the  initial  and  final 
states  respectively. 

Besides  the  thermodynamic  formula  (1)  between  t  and  p, 
numerous  empirical  relations  have  been  proposed  by  different 
investigators.1  Only  one  will  be  mentioned  here,  namely,  that 

i  Winkelmann,  "Handbuch  der  Physik,"  vol.  ii.  2,  p.  702.  Ostwald,  "Lehrbuch 
der  Allgemeinen  Chemie,"  vol.  i.  p.  313. 


PRESSURE    AND    BOILING   POINT 


39 


proposed  by  Regnault  to  represent  his  classical  data  on  a  large 
number  of  saturated  vapors.  By  plotting  temperatures  and  cor- 
responding pressures  on  a  large  scale,  he  found  the  resulting 
curves  could  be  represented  by  interpolation  formulae  of  the 
type 

log  p  —  a  -f-  ?7a* 

where  a,  b,  and  a  are  constants  depending  on  the  nature  of  the 
liquid,  t  =  tc  -f  C,  where  tc  is  the  temperature  in  centigrade 
degrees  and  C  is  a  constant.  He  derives  the  following  values 
for  these  constants  for  the  following  typical  liquids:— 

a  b              log  a  C 

Water          5.42332  —5.46428  0.9972311—1  +20° 

Alcohol        5.54320  -5.01945  0.9972021—1  +20° 

Benzene       4.67667  -4.07461  0.9965676—1  -J-O40 

Apparatus.  —The  arrangement  of  the  apparatus  is  as  follows : 
An  open  manometer  A  is  connected  through  a  large  air  reser- 
voir B,  and  a  return  condenser  C,  with  the  boiling  apparatus 

D.  This  consists  of 
a  horizontal  brass 
cylinder  in  the  axis 
of  which  is  sealed 
a  small  brass  tube 
closed  at  one  end 
for  containing  the 
thermometer  for 
registering  the  tem- 
perature of  the 
boiler. 

The  pressure  in 
the  apparatus  may 
be  varied  by  con- 
necting the  reservoir  #j[with  a  suction  or  a  pressure  pump 
through  the  bottle  F.  This  is  inserted  as  a  trap  to  prevent 
water  from  the  water  pump  from  sucking  back  into  the  appara- 
tus, and  to  collect,  when  the  cock  E  is  opened,  any  water  which 
may  have  condensed  in  B. 


r 


Fig    8. 


40      NOTES  ON  PHYSICAL  LABORATORY  EXPERIMENTS 

The  boiler  is  filled  with  water  through  a  thistle  tube  gauge 
attached  at  one  end;  the  height  of  water  in  the  boiler  is  indicated 
by  the  position  of  the  water  in  this  gauge  which  is  of  glass. 
The  burner  is  constructed  so  as  to  distribute  a  series  of  small 
flames  along  the  length  of  the  boiler. 

Procedure.  —  The  following  directions  apply  particularly  to 
water,  which  is  the  liquid  used  in  this  experiment  :— 

First.  Connect  B  to  the  suction-pump  through  the  safety 
bottle  F  and  exhaust  until  the  pressure  within  the  apparatus  is 
reduced  to  about  50-60  mm.  Close  E  and  the  second  stop-cock 
between  F  and  the  pump.  Then,  and  not  before,  turn  off  the 
water.  See  that  the  apparatus  is  air-tight  (indicated  by  a  con- 
stant reading  of  the  manometer),  before  proceeding  further.  If 
it  is  not,  speak  to  an  instructor. 

Second.  See  that  the  waste-cock  from  the  condenser  is  open 
before  turning  on  the  water  through  C.  It  should  never  be 
closed.  f  Turn  on  the  water,  so  that  a  good  stream  flows  through 
the  condenser. 

Third.  Bring  the  water  in  the  boiler  to  brisk  boiling.  Only 
a  small  flame  will  be  necessary.  The  boiling  point  will  probably 
be  not  more  than  15°  or  20°  above  the  temperature  of  the  room. 
As  soon  as  the  thermometer  indicates  a  constant  temperature, 
record  the  temperature  and  the  height  of  the  mercury  in  the 
manometer. 

Record  also  the  reading  of  the  thermometer  attached  to  the 
manometer,  the  height  of  the  barometer,  and  its  temperature. 
Usually  two  barometer  readings,  one  at  the  beginning  of  the 
experiment  and  one  at  the  end,  will  be  sufficient,  unless  it  is 
changing  very  rapidly,  when  readings  should  be  taken  directly 
before  or  after  recording  the  manometer.  This  completes  all 
data  necessary  for  the  first  set  of  observations. 

Next  allow  air  to  enter  the  apparatus  through  E  until  the 
manometer  indicates  an  increase  of  pressure  of  about  100-150 
mm.  By  thus  increasing  the  pressure,  boiling  will  instantly 
cease  until  the  temperature  has  risen  to  the  new  boiling  point, 
when  a  second  series  of  observations  similar  to  the  above  is  to 
be  taken.  Determine  in  this  manner  the  boiling  points  cor- 


PRESSURE  AND    BOILING   POINT  41 

responding  to  six  or  seven  different  pressures,  taking  the  last 
observation  at  atmospheric  pressure,  or  a  little  above  it.  This 
last  may  be  done  by  forcing  air  into  the  apparatus  at  E  by 
means  of  a  small  force  pump. 

Computation. —  Correct  the  observed  boiling  points  for  ther- 
mometric  errors  (see  table  of  corrections  for  thermometer). 
Reduce  the  corresponding  pressures  in  millimeters  of  mercury 
to  0°  C.,  assuming  the  manometer  scale  (of  seasoned  boxwood) 
to  be  correct  at  ordinary  temperatures.  Plot  the  reduced  data 
with  pressures  as  ordinates,  and  temperatures  as  abscissae.  This 
will  show  graphically  the  relation  between  the  pressure  and  boil- 
ing point  of  the  liquid,  or,  in  other  words,  the  variation  of  the 
presmre  of  its  saturated  vapor  with  the  temperature. 

Ca^ulate  by  equation  (1)  the  specific  volume  of  saturated 
steam,  v2,  at  100°  C.,  and  compare  it  with  the  value  given  in 
Peabody's  Steam  Tables  or  in  Table  VIII.,  Appendix. 

Note. —  To  obtain  the  value  of  ~  at  100°  where  the  vapor 

pressure  curve  will  be  seen  to  be  nearly  linear  over  a  consider- 

AT? 
able  range  of  temperature,  compute  the  approximate  value  -j 

by  taking  two  points  on  the  actual  curve  near  100°,  instead  of 
attempting  to  draw  a  tangent  to  the  curve  at  that  point.  With 
a  thermometer  reading  to  0.001°  C.,  and  a  sensitive  manom- 

Ap 
eter    the    value    of  -j   can    be    obtained    directly    from    the 

observed  data  on  two  boiling  points  with  considerable  accuracy. 
Remember  in  solving  for  v2  in  equation  (1)  that  both  -jr  and 
r  must  be  expressed  in  mechanical  units. 

Problems. —  1.  At  what  pressure  will  an  error  of  0.1 
mm.  in  p  begin  to  affect  the  corresponding  value  of  t  by  0.1° 
C.?  By  0.05°  C.?  (Solve  by  inspection  of  Steam  Tables.) 

2.  Compute  from  formula  (1)  the  melting  point  of  ice 
under  a  pressure  of  ten  atmospheres. 

Given :  latent  heat  of  fusion  of  ice  —  80  calories, 
specific  volume  of  ice  —  1.09  c.cm., 
specific  volume  of  water  at  0°  C.  =•  1.00  c.cm. 

UNIVERSITY 
or 


CALORIMETRY 


GENERAL   DISCUSSION 

This  discussion  should  be  carefully  studied  before  beginning 
any  experimental  work  on  calorimetry. 

Calorimetry  is  the  process  of  measuring  quantities  of  heat. 
The  process  in  general  consists  in  transforming  a  quantity  of 
some  form  of  energy,  as  electrical  energy  or  mechanical  energy 
into  heat  energy,  in  a  vessel  called  the  calorimeter  which  con- 
tains water,  or  some  other  appropriate  liquid,  and  in  measuring 
the  resulting  phenomenon  produced.  By  the  principle  of  the 
conservation  of  energy  the  quantity  of  energy  thus  introduced 
is  equal  to  the  sum  of  all  the  energy  changes  resulting  in  the 
calorimeter,  supposing  the  latter  to  receive  no  other  energy 
from,  or  give  no  energy  to,  the  surroundings.  The  various 
calorimetric  methods  devised  seek  to  reduce  these  energy  changes 
to  the  simplest  and  most  accurately  measurable  forms. 

The  most  common  method,  known  as  the  Method  of  Mix- 
tures, consists  in  introducing  the  energy  directly  into  a  calorim- 
eter containing  a  known  weight  of  water,  in  which  case  the 
phenomenon  to  be  measured  is  simply  the  resulting  rise  of 
temperature  of  the  calorimeter  and  water.  If  this  be  accu- 
rately determined  and  the  weight  and  specific  heat  of  the  water, 
together  with  the  weight  and  the  specific  heat  of  the  calorimeter 
and  all  its  parts  be  known,  the  quantity  of  heat  energy  intro- 
duced into  the  calorimeter  is  given  at  once  by  the  expression  :  — 

q  —  [WoSo.  -f  2  WtSi]  A/  (1) 


where  w0  and  s0  is  the  weight  and  specific  heat,  respectively, 
of  the  water  (s0  may  usually  be  taken  equal  to  unity),  wk;  sk 
are  the  weights  and  specific  heats,  respectively,  of  the  materials 
constituting  the  various  parts  of  the  calorimeter,  and  A£  is  the 
rise  of  temperature  common  to  them  all. 

Simple  as  the  method  is  in  theory  the  quantities  involved  in 
the  measurements  and  the  conditions  to  be  observed  are  such 


CALORIMETRY  43 

that  calorimetric  measurements,  which  are  reliable  to  0.1  per 
cent,  are  among  the  more  difficult  laboratory  processes. 

Units. — The  unit  of  heat  energy  is  the  calorie,  or  more  speci- 
fically the  gram-calorie  or  kilogram-calorie.  It  is  defined  as 
the  quantity  of  heat  required  to  raise  a  unit  mass  (one  gram 
or  one  kilogram)  of  water  through  one  degree  centigrade.  It 
has  been  experimentally  found  that  this  quantity  varies  with 
the  temperature,  hence,  in  order  to  definitely  define  the  cal- 
orie, it  is  necessary  to  further  state  the  particular  temperature 
to  which  it  is  referred.  Owing  to  the  choice  of  various  temper- 
atures by  different  observers,  several  calories  have  come  into 
use  with  the  inevitable  result  of  introducing  great  confusion  in 
the  comparison  of  the  results  of  different  investigators. 

The  universal  adoption  of  one  definite  unit  is  much  to  be 
desired;  but  until  the  use  of  such  a  unit  becomes  general,  a 
definite  statement  of  the  calorie  used  should  always  be  made 
in  expressing  experimental  results  which  have  any  claim  to 
accuracy.  The  following  different  calories  should  not  be  con- 
fused : 

1.  ZERO    DEGREE   CALORIE: — The   quantity   of   heat   required 

to  raise  one  gram  of  water  from  0°  to  1°  C. 

2.  ORDINARY   CALORIE:   cal. — The   quantity   of   heat   required 

to  raise  one  gram  of  water  from  15°  to  16°  C.,  this  being 
taken  as  the  mean  room  temperature. 

3.  MEAN  CALORIE  OR  ICE  CALORIMETER  CALORIE: — The  one- 

hundredth  part  of  the  heat  required  to  raise  one  gram  of 
water  from  0°  to  100°  C. 

4.  OSTWALD'S   CALORIE:   K. — The   quantity   of   heat   required 

to  raise  one  gram  of  water  from  0°  to  100°  C. 

5.  BERTHELOT'S  LARGE  CALORIE:  Cal. — 1000  times  the  ordi- 

nary calorie  as  defined  above. 

The  zero  degree  calorie  is  of  little  or  no  practical  use,  and  is 
to  be  regarded  only  as  a  classical  definition  introduced  by 
Regriault.  The  specific  heat  of  water  in  the  neighborhood  of 
zero  degrees  is  very  difficult  to  determine  with  accuracy,  and 
hence  were  this  unit  adopted,  its  value  would  be  more  uncer- 
tain than  the  calorimetric  measurements  themselves. 


44     NOTES  ON  PHYSICAL  LABORATORY  EXPERIMENTS 

The  ordinary  calorie  denoted  by  cal.  is  that  most  frequently 
adopted,  as  most  calorimetric  measurements  are  carried  out  at 
"room  temperature,"  which  is  variously  taken  from  15°  to  18°  C. 
The  calorie  is  nearly  constant  throughout  this  range  of  temper- 
ature. 

The  mean  calorie  or  ice  calorimeter  calorie  has  been  used 
chiefly  in  expressing  results  obtained  with  the  ice  calorimeter, 
which  is  usually  calibrated  by  the  quantity  of  heat  given  out 
by  water  cooling  from  100°  to  O6.  This  unit  does  not  differ 
from  the  ordinary  calorie  by  more  than  0.14  per  cent. 

Ostwald,  following  the  suggestion  of  Schuller  and  Wartha, 
has  proposed  the  100  times  greater  unit  denoted  by  K,  as  being 
not  only  of  a  more  convenient  magnitude  for  expressing  thermo- 
chemical  data,  but  also  more  rational  than  the  somewhat  ar- 
bitrary ordinary  calorie.  Its  advantage  as  a  thermo-chemical 
unit  of  heat  measurement  will  be  seen  from  the  following  ex- 
ample: The  heat  of  combustion  of  one  atomic  weight  (12 
grams)  of  carbon  to  carbon  dioxide  is  97000.  cal.,  but  as  thermo- 
chemical  data  are  seldom  reliable  to  more  than  0.1  per  cent, 
i.e.,  to  four  significant  figures,  the  superfluous  ciphers  necessary 
to  fix  the  decimal  point  may  be  avoided  by  using  the  larger 
Ostwald  calorie  K,  and  writing  the  above  quantity  of  heat  970 
K.  For  the  same  reason  Berthelot  adopts  the  still  larger  unit 
1  Cal.  =  1000  cal.  for  expressing  the  results  of  his  thermo- 
chemical  investigations.  Ostwald's  calorie  is  in  general  use  in 
Germany;  Berthelot's  in  France. 

From  the  most  recent  determinations  of  the  variation  of  the 
specific  heat  of  water  with  the  temperature,  the  following  re- 
lations hold  between  the  various  calories  above  defined: 

1  zero  degree  calorie  —  1.008  ordinary  (15°  -  16°)  calories.1 
1  mean  calorie  =  1.0014  ordinary  (20°)  calories.2 
In  absolute  units  1  ordinary  (15°)  calorie  =  g  J  ergs 

—  980.6  X  42730  ergs 

=  4.190  X  107  ergs 

J  —  42730  gram-centimeters  at  sea   level,  45°  latitude 
(g  =  980.6),  and  referred  to  the  ordinary  calorie. 

1  Liidin,  Wied.  Beiblatter,  9O,  764, 1896. 

2  Callander  and  Barnes,  Phys.  Rev.,  1O,  213,  1900. 


CALORIMETRY  45 

Sources  of  Error. —  The  principal  sources  of  error  which  arise 
in  calorimetry,  and  which  in  accurate  work  must  be  corrected 
for  or  rendered  negligible  by  special  adjustment  of  the  condi- 
tions of  the  experiment,  are  the  following: 

First.— Errors  in  Thermometry.  The  rise  of  temperature  in 
a  calorimetric  measurement  is  in  most  cases  small  —  a  few  de- 
grees only — hence  thermometers  sensitive  to  at  least  0.01°  C. 
are  usually  required.  When  the  rise  of  temperature  is  very 
small,  a  few  tenths  of  a  degree  only,  thermometers  indicating 
differences  of  temperature  of  0.005°  or  even  0.001°  are  required. 
The  calibration  errors  and  scale  unit  of  such  calorimeter  ther- 
mometers must  be  carefully  determined,  as  well  as  the  cor- 
rections for  all  other  thermometers  used  in  the  work. 

Second. — Errors  arising  in  the  determination  of  the  heat  ca- 
pacity or  water  equivalent  of  the  calorimeter.  By  this  is  under- 
stood the  value  of  the  term  ^wksk  in  formula  (1),  that  is,  the 
total  heat  capacity  of  all  parts  of  the  calorimeter  and  its  con- 
tents, exclusive  of  the  water.  This  is  called  the  "water  equiv- 
alent" of  the  calorimeter,  since  this  number  of  grams  of  water 
(specific  heat  unity),  would  be  raised  through  the  same  tem- 
perature as  the  material  in  question  by  the  same  quantity  of 
heat.  If  the  weights  and  specific  heats  of  all  parts  of  the 
calorimeter  are  known  with  sufficient  accuracy,  the  water 
equivalent  can  be  computed  at  once,  in  which  case  the  calori- 
metric measurement  is  a  primary  one.  If,  on  the  other  hand, 
these  data  are  not  known  with  sufficient  accuracy,  the  water 
equivalent  has  to  be  experimentally  determined,  and  the  meas- 
urement is  then  a  secondary  one. 

It  is  always  desirable  that  the  water  equivalent  of  the  calo- 
rimeter be  as  small  as  possible  in  comparison  with  the  weight 
of  water  used.  The  material  of  which  a  calorimeter  is  Con- 
structed should  therefore  be  as  thin  as  is  consistent  with  rigidity, 
and  should  have  as  low  a  specific  heat  as  possible.  It  is  also 
desirable  that  it  have  a  high  thermal  conductivity  in  order  to 
assume  quickly  the  mean  temperature  of  the  water,  and  for 
reasons  mentioned  below,  it  should  also  be  capable  of  a  high 
polish.  The  metals  best  fulfilling  these  conditions  will  be  seen 
from  the  following  table: 


Platinum 

Sp.  Heat 

0.032 

Density 

21.5 

Product 

0.69 

Silver 

0.056 

10.5 

0.59 

Nickel 

0.11 

8.9 

0.98 

Copper 
Glass 

0.093 
0.20 

8.9 
2.4 

0.83 
0.48 

Mercury 

0.033 

13.6 

0.45 

46      NOTES  ON  PHYSICAL  LABORATORY  EXPERIMENTS 

Thermal  Conductivity 

109. 

82. 
0.13 
2. 

It  appears  from  the  above  table  that  silver  and  platinum  are 
the  metals  best  adapted  for  constructing  calorimeters,  both  on 
account  of  their  low  specific  heat  and  high  thermal  conduc- 
tivity. Platinum  is  the  more  durable,  and  is  especially  adapted 
for  thermo-chemical  experiments  involving  the  use  of  acids  and 
bases  which  attack  other  metals.  Gold-plated  silver  calorim- 
eters may,  however,  often  be  used  for  such  experiments  and 
are  much  cheaper.  Glass  is  not  to  be  recommended  on  account 
of  its  very  low  thermal  conductivity,  which  is  only  about  one- 
thousandth  that  of  silver.  Nickel,  or  nickel-plated  copper  may 
be  used  with  non-corrosive  liquids. 

The  exact  computation  of  the  heat  capacity  of  the  bulb  and 
immersed  portion  of  the  calorimeter  thermometer  is  usually 
impossible,  as  the  weight  of  mercury  and  glass  cannot  sepa- 
rately be  known.  It  happens  fortunately,  however,  that  the  heat 
capacity  of  an  equal  volume  of  mercury  and  of  glass  is  nearly 
the  same,  0.45  and  0.48,  respectively  (see  above  table).  Hence 
the  heat  capacity  of  the  immersed  portion  of  a  thermometer 
may  be  computed  with  very  close  approximation  as  the  pro- 
duct of  the  mean  of  these  values,  namely  0.465,  times  the  total 
volume  of  the  part  of  the  thermometer  which  is  immersed. 

Third. — Errors  arising  from  exchange  of  heat  by  conduction 
and  radiation.  As  every  calorimetric  measurement  requires 
time  for  its  completion,  the  calorimeter  and  contents  will  gain 
or  lose  a  certain  quantity  of  heat  by  conduction  and  radiation 
from  or  to  the  surroundings,  unless  the  surroundings  are  main- 
tained exactly  at  the  temperature  of  the  calorimeter  through- 
out the  experiment.  As  the  temperature  is  continually  chang- 
ing, this  condition  cannot  in  general  be  realized,  and  hence 
corrections  must  be  made  for  these  two  sources  of  error.  Gain 


CALORIMETRY  47 

or  loss  of  heat  by  conduction  may  be  practically  eliminated  by 
supporting  the  calorimeter  on  three  non-conducting  points 
such  as  corks,  or  resting  it  on  a  net-work  of  strings.  If  the 
calorimeter  could  be  vacuum  jacketed,  practically  all  exchange 
of  heat  by  conduction  or  convection  would  be  eliminated. 

The  errors  due  to  radiation  are  however  more  serious,  and 
constitute  one  of  the  most  troublesome  sources  of  error  met 
with  in  calorimetric  work.  The  quantity  of  heat  radiated  (or 
absorbed)  by  a  surface  is  proportional  to: 

1.  The  area  of  the  radiating  surface. 

2.  A  constant  depending  on  the  nature  of  the  radiating  sur- 

face. 

3.  The  difference  of  temperature  between  the  surface  and 

surroundings. 

4.  The  time  during  which  radiation  takes  place. 

The  radiating  surface  should  therefore  be  as  small  as  is  con- 
sistent with  the  required  volume.  Calorimeters  are  usually 
cylindrical  in  form,  and  hence  for  a  closed  calorimeter,  i.e., 
one  provided  with  a  cover,  the  best  relative  dimensions  would 
be  height  =  diameter.  They  are  usually,  however,  made  with 
the  diameter  considerably  smaller  in  proportion  than  this,  in 
order  to  diminish  the  area  of  the  surface  of  the  liquid  exposed  to 
evaporation.  Calorimeters  of  less  than  400-500  cubic  centime- 
ters capacity  are  not  to  be  recommended  except  for  special  work. 

The  numerical  value  of  the  radiation  factor  depends  upon 
the  degree  of  polish  of  the  radiating  surface.  If  the  surface 
is  rough  and  tarnished  the  coefficient  is  large,  being  a  maxi- 
mum for  a  "perfectly  black"  surface.  On  the  other  hand, 
it  may  be  reduced  to  a  very  small  value  by  giving  the  surface 
of  the  calorimeter  the  highest  possible  burnish.  To  still  further 
reduce  this  source  of  error  the  calorimeter  should  be  enclosed 
within  a  second  vessel  or  jacket  whose  inner  walls  are  also  bur- 
nished. The  third  and  fourth  factors  show  that  the  temper- 
ature of  the  calorimeter  should  not  differ  very  greatly  from 
that  of  the  surroundings,  and  that  the  duration  of  the  experi- 
ment should  be  as  short  as  is  consistent  with  other  conditions. 
If  the  difference  in  temperature  between  calorimeter  and  sur- 


48 


NOTES  ON  PHYSICAL  LABORATORY  EXPERIMENTS 


roundings  amounts  to  more  than  about  10°  C.,  the  conditions 
enumerated  above,  which  are  a  statement  of  Newton's  Law  of 
Cooling,  no  longer  hold  true.  In  what  follows  it  will  be  assumed 
that  the  temperature  difference  does  not  exceed  this  amount. 

Cooling  Correction.  —  Let  us  now  investigate  how  the  heat 
lost  or  gained  by  radiation  may  be  allowed  for  or  eliminated. 
This  correction  is  generally  known  as  the  "cooling  correction." 
A  calorimetric  measurement  consists  in  general  of  the  three  fol- 
lowing continuous  operations: 

First.  Preliminary  readings  of  the  temperature  of  the  water 
in  the  calorimeter  every  half  minute  for  at  least  five  minutes 
immediately  preceding  the  operation  proper. 

Second.  The  operation  proper,  consisting  of  introducing  heat 
into  the  calorimeter,  e.g.,  dropping  in  a  hot  substance  as  in 
"Specific  Heat/'  or  passing  in  steam  as  in  "Latent  Heat,"  or 
heating  a  coil  of  wire  by  an  electric  current  as  in  "Mechanical 
Equivalent." 

Third.  Final  temperature  readings  after  the  operation  has 
ended,  continuing  at  half  minute  intervals  for  at  least  another 
five  minutes  (better  for  eight  or  ten  minutes),  these  data  to 
serve  for  determining  the  final  rate  of  gain  or  loss  of  heat. 

The  preliminary  readings  furnish  data  for  finding  the  tem- 
perature (which  in  general  cannot  be  read),  at  the  moment  of 
beginning  the  operation,  and  for .  determining  the  rate  of  gain 
or  loss  of  heat  of  the  calorimeter  at  that  time. 

If  the  data  thus  obtained  be  plotted  with  temperatures  as 
ordinates  and  times  as  abscissa?,  curves  of  the  following  general 
type  will  be  obtained: 


& 


Fig 


CALORIMETRY  49 

Curve  a,  figure  9,  represents  the  general  case  in  which  the 
calorimeter  gains  heat  from  the  surroundings  from  A  to  B; 
the  operation  begins  at  B  and  heat  is  developed  within  the 
calorimeter  until  the  temperature  has  risen  to  C;  at  C  the  oper- 
ation ceases,  but  if  certain  parts  of  the  calorimeter  or  its  con- 
tents have  become  heated  above  the  mean  temperature  of  the 
calorimeter,  there  will  then  result  a  further  rise  of  temperature 
due  to  the  equalization  of  temperature  between  such  hot  parts 
and  the  water  of  the  calorimeter,  or  between  the  water  and 
the  metal  of  the  calorimeter  itself.  This  will  be  represented 
by  the  portion  of  the  curve  CD,  D  being  the  temperature  at 
which  the  whole  calorimeter  and  contents  arrive  at  a  uniform 
temperature.  If  D  is  above  the  temperature  of  the  surround- 
ings, as  is  usually  the  case,  the  calorimeter  will  then  give  up 
heat  to  the  surroundings  by  radiation  at  a  uniform  rate  repre- 
sented by  the  straight  line  DE.  The  temperature  D  marks  the 
beginning  of  this  straight  line  which  should  be  tangent  to  the 
curve  CD  at  D. 

In  certain  operations,  as  in  the  development  of  heat  in  the 
calorimeter  by  heating  a  coil  of  wire  by  a  current  (as  in  "Me- 
chanical Equivalent"),  or  in  condensing  steam  in  the  calo- 
rimeter (as  in  "Latent  Heat")  the  portion  CD  of  curve 
a  may  become  very  small  as  in  curve  6,  very  little  rise  of  tem- 
perature occurring  after  the  operation  ceases.  On  the  other 
hand,  when  a  heated  mass  is  suddenly  introduced  into  the  cal- 
orimeter (as  in  "Specific  Heat"),  the  whole  operation  consists 
of  an  equalization  of  temperature,  and  B  and  C  fall  together. 
In  this  case  CD  may  take  any  form  between  a  curve  of  type 
c  and  a  nearly  straight  line,  as  in  curve  d,  according  to  the  ve- 
locity with  which  the  equalization  of  temperature  takes  place. 
If  the  substance  introduced  is  a  good  conductor  and  has  a 
large  surface  compared  with  its  mass,  e.g.,  if  it  is  cut  up  into 
small  pieces,  the  curve  will  be  of  the  form  d.  If,  however,  the 
substance  is  a  single  large  mass  of  poorly  conducting  material, 
such  as  vulcanite  or  glass,  the  curve  will  take  the  form  c. 

In  order  that  curves  similar  to  the  above  types  may  be  ob- 
tained, it  is  absolutely  essential  that  the  stirring  be  so  efficient 


50      NOTES  ON  PHYSICAL  LABORATORY  EXPERIMENTS 

and  the  thermometer  so  placed  in  the  calorimeter,  that  the 
temperature  indicated  is  the  mean  temperature  of  the  calorim- 
eter and  contents  as  a  whole,  at  the  time  of  observation. 
Irregularities  in  the  curves  can  almost  invariably  be  traced  to 
failure  to  fulfil  one  or  both  of  these  conditions.  Thus  a  hump 
in  the  curve  at  D  indicates  that  the  bulb  of  the  thermometer 
has  been  unduly  heated  by  too  close  proximity  to  the  source  of 
heat.  In  all  such  cases  the  data  should  be  rejected. 

Demonstration.  —  It  will  now  be  shown  how  the  cooling  cor- 
rection can  be  computed,  first  for  the  general  case  represented 
by  a,  figure  9,  and  then  for  several  special  cases. 

General  case.  Let  rl  be  the  rate  of  exchange  of  heat  of  the 
calorimeter  in  degrees  per  minute,  reckoned  plus  for  gain  and 
minus  for  loss  of  heat,  as  deduced  from  the  tangent  of  the 
straight  line  best  representing  the  temperatures  between  A 
and  B.  Let  ^  =  the  temperature  at  the  instant  the  operation 
begins  at  B,  and  &i,  the  corresponding  time.  Note  that  since 
one  observer  can  seldom  read  this  temperature  at  the  time  of 
performing  the  operation,  it  must  be  obtained  by  extrapolating 
the  line  AB  to  the  time  0l7  at  which  the  operation  begins.  Sim- 
ilarly let  r2  be  the  rate  of  exchange  at  the  final  temperature  tz 
at  the  time  02,  i.e.,  the  temperature  and  time  corresponding 
to  the  point  D.  Let  ta  be  the  mean  temperature  of  the  sur- 
roundings. The  calorimeter  then  gains  heat  from  the  sur- 
roundings up  to  a  time  Oa  when  its  temperature  reaches  that  of 
the  surroundings,  after  which  it  begins  to  lose  heat. 

By  Newton's  law  of  cooling  the  rate  at  which  a  body  gains 
or  loses  heat  by  radiation  is  directly  proportional  to  the  differ- 
ence of  temperature  between  the  body  and  its  surroundings. 
Applied  to  a  calorimeter,  if  its  heat  capacity  does  not  sensibly 
vary  during  the  operation,  we  may  assume  that  its  rate  of  loss 
or  gain  of  heat  is  proportional  to  its  rate  of  rise  or  fall  of  tem- 
perature. This  assumption  is  made  in  the  following  demon- 
stration : 

Let  the  temperature  change  per  unit  time  at  any  tempera- 
ture t  be  denoted  by  r.  Then  r  =  a  (tn  —  0  where  a  is  a  con- 
stant depending  on  the  nature  of  the  given  calorimeter. 


CALORIMETRY  51 

The  total  rise  in  temperature  due  to  radiation  during  the 
interval  from  01  to  02  will  be  therefore 

r#2  Ch  r     Ce*  Ch     ~i 

I     rdO  =  a  I      (ta  —  t)  dO  =  a  \ta  I     do  -     I     tdO 

JQ\  J9\  [_    *J9\  ,        «/#i 

=  a  [4,  (fl,  -  «,)  -jjp  /  (6)  d»]  .  (1) 

/*02 

But    I     /  (0)   e?0  is   the  area  bounded    between  the  curve 

*J6\ 

the  ordinates  at  6l  and  02,  and  the  axis  of  6.  Its  approximate 
value  may  be  found  by  computing  the  mean  value  of  the  ordi- 
nate  tm,  i.e.,  the  mean  value  of  the  temperature  between  t1  and 
/2,  and  multiplying  by  the  time  interval  02  —  0lt 

t    -    —  f-  4-  6  4-  c  +        4-  -1 
"n-lL2  2j 


where  a,  6,  ...  n  are  temperature  readings  taken  from  the  plot 
or  data  at  the  time  6l  and  each  following  half  minute  up  to  02r 
respectively.  Hence  the  approximate  value  of  formula  (1) 
becomes 


rdO  =  a 


J  =  a  (ta—  tm)  (02—  ^), 


which  taken  with  opposite  sign  is  the  correction  due  to  radia- 
tion to  be  added  to  the  observed  rise  in  temperature.  The 
corrected  rise  of  temperature  is  therefore 

t2  —  t1  +  a(t,H  —  ta)  (02  —  0i).  (2) 

This  formula  is  general  and  can  be  applied  to  a  plot  of  calori- 
metric  data  of  any  form. 

The  radiation  factor  a  can  be  determined  at  once  from  the 
simultaneous  equations 

TI  =  a  (t,  —  /j) 

7*2  ~—  &  (t(t          '2) 

whence 


52      NOTES  ON  PHYSICAL  LABORATORY  EXPERIMENTS 

The  mean  temperature  of  the  surroundings  ta  can  be  ob- 
served, or  it  may  be  computed  from  the  above  equations  as 

^  =  ti+~  or;4=^V+  ^ 

It  is  evident  from  the  above  deduction  that  the  correction 
term  in  (2)  becomes  zero  when  tm  =  ta.  By  preliminary  ex- 
periments on  the  actual  rise  of  temperature  occurring  in  the 
experiment,  it  is  possible  to  calculate  what  the  initial  tempera- 
ture of  the  water  below  the  temperature  of  the  surroundings 
should  be  in  order  that  this  condition  may  be  fulfilled,  and  the 
extra  labor  thus  involved  is  in  many  experiments  warranted. 

Special  Case  I.  —  The  Rumford  Method.  The  total  rise  of 
temperature  is  at  a  uniform  rate. 

If  the  rise  of  temperature  is  uniform  during  the  whole 
operation,  and  the  part  CD  of  the  curve  is  negligible  com- 
pared with  BC,  i.e.,  C  and  D  practically  coincide,  the  mean 

temperature  tm  will  evidently  be  tm  —  1  ~}~  2  .     Hence  if  the 

initial  temperature  of  the  water  is  brought  to  just  as  many 
degrees  below  the  temperature  of  the  surroundings  ta,  as  the 
final  temperature  is  allowed  to  rise  above  this  temperature, 
then  tm  =  ta  and  the  gain  and  loss  of  heat  during  the  opera- 
tion will  practically  offset  each  other.  The  observed  rise  of 
temperature  will  therefore  be  the  correct  one.  This  is  known 
as  the  Rumford  Method  of  eliminating  the  cooling  correction. 
It  is  to  be  especially  noted  that  it  is  only  applicable  when  the 
•entire  rise  of  temperature  is  at  a  uniform  rate,  for  only  then  is 


If  in  the  above  case  the  initial  and  final  temperatures  are 
not  so  adjusted  with  respect  to  the  surroundings  that  tm  =  ta, 
i.e.,  TI  is  not  exactly  equal  to  r2,  it  is  easy  to  show  that  the  cor- 
rection to  be  applied  (i.e.,  added)  is 

-^i"'  («,-«i).  (3) 


CALORIMETRY 


53 


For  suppose  the  data    to    be   represented    as   in   figure  10. 
If  ta  is  the  mean  temperature  of  the  surroundings,  the  loss 

of  heat  during  the  time  the 
temperature  rises  from  ta  to 
t2  will  be  exactly  compensated 
by  gain  of  heat  during  the  in- 
terval it  is  rising  from  some 
temperature  tx  to  ta  where  tx 
is  just  as  far  below  ta  as  tz 
is  above  it.  The  resultant  cor- 
rection will  therefore  be  the 
gain  of  heat  during  the  period 
01  to  Ox  while  the  tempera- 
ture is  rising  from  ^  to  tx.  This  may  be  found  at  once  by 
substituting  in  the  general  formula  (1).  We  obtain  for  the 
correction 


This  may  be  written 
(fr- 


1   T"   tj: 


and    -fnf— -fllT 

f.r      4       ta      h 


But         (,.  =  ta  —  (t2  —  ta)  =  2ta  — 
hence  the  correction  reduces  at  once  to 


/*!  and  r2  are  obtained  by  finding  the  tangent  of  the  angle 
which  the  straight  lines  best  representing  the  preliminary  and 
final  readings,  make  with  the  axis  of  0  respectively.  They  are 
to  be  algebraically  added,  gain  of  heat  being  reckoned  positive, 
and  loss  of  heat  negative. 


\  '3  R  A 
O-    THE      ' 

UNIVERSITY 

or 


54 


NOTES  ON  PHYSICAL  LABORATORY  EXPERIMENTS 


Special  Case  II. —  The  rise  of  temperature  from  B  to  C  is 
uniform,  but  the  portion  of  the  curve  CD,  although  small,  is 

not  negligible  compared  with  BC,  fig- 
ure 11.  Then,  since  the  rate  of  ex- 
change during  the  interval  CD  is 
practically  r2,  the  temperature  would 
have  risen  to  C'  had  the  equalization 
of  heat  from  C  to  D  been  instantaneous, 
where  C"  is  the  intercept  of  DE  ex- 
tended back  to  the  ordinate  through 
C.  Call  this  temperature  /'2.  The 
cooling  correction  for  the  interval  BC 
is  that  already  deduced  under  Special 
Case  I.  Hence  the  corrected  rise  of  temperature  will  be 


t  _    y  JJI   /-£/  /)    \ 

2          61  "2          ^     2  ly^ 


(4) 
the  abscissa  of 


where  0^  is  the  time  corresponding  to  £'2? 
the  point  C  or  Cf '. 

Special  Case  III. — The  rise  of  temperature  .during  the  oper- 
ation is  uniform,  and  the  initial  temperature  is  so  adjusted 
that  r2  =  0,  i.e.,  DE  is  horizontal.  This  is  evidently  a  special 
case  of  the  above,  and  the  corrected  rise  of  temperature  is 


t  2  ti y  (0  ^  


(5) 


Special  Case  IV. — When  the  equalization  of  temperature 
CD  is  slow,  as  in  c,  figure  1,  or  constitutes  a  considerable  por- 
tion of  the  total  rise,  it  is  advantageous  to  so  adjust  the  initial 
temperature  that  the  final  temperature  /2  coincides  as  nearly  as 
may  be  with  the  temperature  of  the  surroundings,  i.e.,  so  that 
r2  =  0.  The  correction  is  to  be  computed  by  the  general 
formula.  This  procedure  not  only  reduces  the  magnitude  of 
the  rate  r2  most  affecting  the  correction,  but  also  serves  to  de- 
termine it  with  greater  accuracy. 


SPECIFIC  HEAT  OF  SOLIDS 


55 


SPECIFIC    HEAT    OF    SOLIDS 

THE    METHOD    OF   MIXTURES 

Object. —  The  object  of  this  experiment  is  to  determine  the 
specific  heat  of  a  solid  substance  by  the  Method  of  Mixtures 
to  about  0.5  per  cent.  The  experiment  illustrates  the  general 
procedure  in  a  simple  calorimetric  measurement,  the  further 
application  of  various  matters  discussed  under  thermometry, 
and  the  method  of  applying  the  cooling  correction. 

Apparatus. —  The  apparatus  used  is  shown  in  figure  12.  It 
consists  of  an  open  calorimeter  C  of  burnished  nickel-plated 
copper  which  rests  on  cork  supports  inside  a  similar  nickel 

plated  vessel  or 
jacket;  a  stirrer  S 
of  the  same  ma- 
terial is  also  pro- 
vided. The  calori- 
meter thermome- 
ter 77for  measuring 
£  the  rise  in  tempera- 

ture is  held  in 
place. by  a  support 
fixed  to  the  jacket. 
The  calorimeter  is 
protected  from  the 
aa  heat  and  the  steam 
of  the  boiler  by  a 
double  walled  screen  W  open  at  the  bottom  and  top  to  permit 
free  circulation  of  air. 

The  heating  apparatus  consists  of  a  boiler  B,  on  the  top  of 
which  is  placed  the  heater  proper,  H.  This  consists  of  two 
concentric  brass  cylinders  joined  at  the  top.  The  inner  cylin- 
der is  closed  at  the  bottom  and  forms  a  receptacle  for  the  sub- 
stance to  be  heated.  The  bottom  of  the  larger  outer  cylinder 
terminates  in  a  conical  tube  by  means  of  which  it  is  connected 
with  the  boiler.  The  steam  passes  up  around  the  inner  cylinder 


ms 


56  NOTES   ON    PHYSICAL    LABORATORY    EXPERIMENTS 

and  escapes  through  a  small  side  tube  at  the  top.  The  outer 
cylinder  is  heavily  lagged  with  felt  to  prevent  loss  of  heat  and 
to  facilitate  handling  while  hot.  The  substance  to  be  heated 
is  placed  in  the  inner  cylinder  which  is  then  closed  by  a  cork 
or  rubber  stopper,  through  which  the  bulb  of  the  thermometer 
for  taking  the  temperature  of  the  substance  should  pass  easily. 
The  upper  part  of  this  thermometer  which  projects  beyond 
the  stopper  is  enclosed  in  a  "stem  exposure"  tube  P  (see  page 
23)  filled  with  water,  the  temperature  of  which  is  determined 
by  an  auxiliary  thermometer  not  shown  in  the  figure.  The 
corrections  for  all  thermometers  used  with  the  apparatus  are 
given  on  their  cases. 

Procedure. —  Place  the  substance  in  the  heater  and  begin 
heating  it  up  at  once,  as  the  longest  part  of  this  experiment 
consists  in  allowing  the  substance  to  reach  a  uniform  high 
temperature.  See  that  the  graduations  on  the  thermometer 
which  is  used  for  taking  the  temperature  of  the  substance  are 
distinctly  visible  from  90°-100°.  If  not,  rub  in  some  lead  with 
a  soft  pencil.  If  this  precaution  is  not  observed,  difficulty 
may  be  encountered  in  reading  the  thermometer  afterwards 
when  it  is  immersed  in  water.  Arrange  the  thermometer  and 
stem  exposure  tube  as  shown  in  the  figure.  Record  where  the 
thermometer-  enters  the  tube  as  datum  for  determining  the 
stem  exposure  correction. 

While  the  substance  is  heating,  weigh  the  calorimeter  and 
the  stirrer,  dry.  Next  fill  the  calorimeter  to  about  three-fourths 
its  capacity  with  water  and  weigh.  Ordinary  tap  water  may 
be  used.  As  the  exact  rise  of  temperature  is  unknown,  it  is 
not  possible  in  a  single  experiment  to  adjust  the  initial  temper- 
ature of  the  water  to  the  best  point  below  that  of  the  surround- 
ings. The  apparatus  is  so  designed,  however,  that  the  rise  of 
temperature  with  the  substances  employed  is  about  4°  or  5°. 
Moreover  the  substance  used  is  metal,  and  is  divided  into  a 
number  of  small  pieces  so  that  the  equalization  of  heat  between 
it  and  the  calorimeter  is  very  rapid.  The  plotted  data  will  give 
a  curve  similar  to  that  in  d,  figure  1.  With  this  knowledge  it 
is  best  to  adjust  the  water  in  the  calorimeter  to  about  two  or 


SPECIFIC  HEAT   OF  SOLIDS  57 

three  and  one-half  degrees  below  the  temperature  of  the  sur- 
roundings, i.e.,  the  temperature  indicated  by  a  thermometer 
(the  calorimeter  thermometer  may  be  used),  placed  within 
and  touching  the  side  of  the  jacket  surrounding  the  calorimeter. 
If  a  preliminary  experiment  should  show  the  equalization  of 
temperature  to  take  place  slowly,  as  in  the  case  of  poorly  con- 
ducting substances,  the  initial  conditions  should  be  adjusted  a& 
described  under  special  case  IV,  p.  54. 

A  blank  form  should  next  be  prepared  for  recording  data 
with  one  column  for  the  time  in  hours,  minutes  and  seconds, 
and  another  for  the  corresponding  temperature  readings.  The 
times  should  be  written  down  beforehand  in  half-minute  inter- 
vals for  a  period  of  at  least  fifteen  minutes.  Such  a  previously 
prepared  blank  is  of  great  assistance  in  taking  down  data  of 
this  kind,  as  it  lessens  the  labor  during  the  operation,  dis- 
tracts the  attention  of  the  observer  less  from  his  temperature 
readings,  and  in  case  any  observations  are  omitted,  greatly 
lessens  the  confusion  in  recording  subsequent  data  in  their 
proper  place. 

When  the  temperature  of  the  heated  substance  becomes 
constant,  and  not  before,  begin  taking  the  thermometer  read- 
ings. Record  first  with  the  calorimeter  thermometer  the  tem- 
perature ts  of  the  surroundings  (inside  of  the  jacket).  Then 
place  the  thermometer  in  the  calorimeter  and  with  regular  and 
constant  stirring  (a  long  and  not  too  rapid  up  and  down 
motion),  begin  the  "preliminary  readings,"  continuing  the  same 
for  at  least  five  minutes.  The  thermometer  should  be  read  to 
0.01°  C.  Suppose,  for  illustration,  that  the  first  reading  was  at 
2  h.  35  min.  0  sec.  At  the  end  of  five  minutes,  i.e.,  after  the 
reading  at  2  h.  40  min.  0  sec.,  suspend  readings  of  the  calorim- 
eter thermometer  and  prepare  for  the  operation  proper.  First, 
read  the  temperature  of  the  stem  exposure  thermometer  and 
remove  it.  Second,  read  very  carefully  the  temperature  of  the 
hot  substance.  Third,  remove  the  thermometer  with  its  at- 
tached stem  exposure  tube  from  the  heater  and  place  it  in 
the  support  R.  In  this  operation  do  not  remove  the  cork 
closing  the  heater;  otherwise  the  substance  will  become  some- 


58      NOTES  ON  PHYSICAL  LABORATORY  EXPERIMENTS 

what  cooled.  These  operations  can  be  easily  made  without 
undue  haste  during  the  minute  from  2  h.  40  min.  0  sec.  to  2  h. 
41  min.  0  sec.  A  few  seconds  before  the  latter  minute  expires 
remove  the  heater  from  the  boiler,  and  exactly  on  the  41st 
minute  take  out  the  stopper  and  pour  the  hot  substance  into 
the  calorimeter.  The  calorimeter  thermometer  should  be  so 
placed  that  the  substance  is  poured  away  from  its  bulb,  not 
only  to  prevent  accident,  but  also  to  avoid  local  heating  of 
the  water  in  the  neighborhood  of  the  bulb.  It  is  safer  during 
this  operation  to  raise  the  thermometer  out  of  the  calorimeter 
entirely.  Immediately  after  the  transfer  resume  stirring  the  con- 
tents of  the  calorimeter  as  thoroughly  as  possible.  The  success 
of  the  experiment  from  this  point  on  depends  largely  on  the 
efficiency  of  the  stirring.  Read  the  calorimeter  thermome- 
ter one-half  minute  after  the  operation,  i.e.,  at  2  h.  41  min.  30 
sec.,  and  on  every  following  half-minute  for  eight  or  ten  min- 
utes, stirring  of  course  constantly.  This  completes  the  calori- 
metric  observations.  There  still  remains  only  to  determine 
the  weight  of  the  substance  dry. 

At  the  conclusion  of  the  experiment  replace  the  substance 
(dry),  all  three  thermometers,  and  stem  exposure  accessories, 
in  their  case  and  return  the  same  to  the  instructor. 

Computation. —  First.  Make  a  plot  of  the  temperature  and 
time  observations,  and  from  it  determine  the  cooling  correc- 
tion. The  form  of  the  curve  obtained  will  determine  which 
method,  pp.  52-54,  it  is  best  to  apply.  The  temperature  ^  of 
the  calorimeter  at  the  instant  of  inserting  the  hot  substance  is 
also  to  be  determined  from  the  plot. 

Second.  Compute  the  temperature  tt  of  the  hot  substance 
at  the  time  of  introduction  into  the  calorimeter,  applying  cali- 
bration and  stem  exposure  corrections  to  the  observed  reading. 
See  p.  23. 

Third.  Calculate  the  water  equivalent  of  the  calorimeter, 
k  =  w1sl  -f-  w2s2  -f-  .  .  .  =  2  w^t.  The  specific  heat  of  the 
material  of  the  calorimeter  may  be  taken  as  0.095.  The  water 
equivalent  of  the  immersed  thermometer  is  readily  shown  to  be 
negligible  in  this  experiment. 


SPECIFIC    HEAT    OF    SOLIDS  59 

Fourth.  Compute  from  the  above  data  the  specific  heat  of 
the  substance.  The  formula  for  computing  the  specific  heat 
by  the  method  of  mixtures  is 

(w0  +  A:)  (L  —  ti) 


where     6-  =  specific  heat  of  substance; 
w  =  weight  of  substance; 
u\,  =.  weight  of  water; 

wly  w2,  etc.  =  weights  of  various  parts  of  calorimeter; 
>?!,  s2,  etc.  —  specific   heats  of  various  parts  of  the  calo- 
rimeter; 

t,  —  t2  =  corrected  fall  of  temperature  of  substance ; 
/2  -  tl  —  corrected  rise  of  temperature  in  calorimeter. 

Precision  Discussion. —  If  each  parenthesis  in  the  above  formula 
be  regarded  as  a  single  independent  variable,  the  formula  for  s  can 
be  treated  as  a  simple  product  and  quotient  of  four  variables, 
namely,  the  rise  of  temperature  of  the  calorimeter  and  contents, 
the  fall  of  temperature  of  the  substance,  the  weight  of  the  substance, 
and  the  weight  of  the  water  plus  the  water  equivalent  of  the  cal- 
orimeter. Suppose  it  is  desired  to  determine  s  to  0.5  per  cent. 
What  will  be  the  allowable  deviations  in  these  four  compoments? 

Solving  for  "Equal  Effects"  we  have  at  once 

8(w0  +  k)  _  S(to  —  fr)  _  Sw  _  S(ts  —  <2)  _     1       ds  _  0.005 
Wo  +  k    '  '    t2  —  ti          iv  ~'    ts  —  tt    ~  ^/4~     -s  2 

All  four  factors  must  therefore  be  measured  to  0.25  per  cent. 
With  the  apparatus  provided  the  following  approximate  values- 
may  be  assumed  for  illustration.  Suppose 

w  —  300  gnis.  then  dw  =  0.75  gm. 

Wo  +  k  =  500  gms.  "  8(w0  +  A;)  =  1 .2  gms. 

t*  —  h  =  20°  —  1 5°  =  5°  5(^2  —  *i)  =  0.013°. 

f»  — *2=100°  — 20°  =  80°  "  S(ts~ -tz)  =  0.20°. 

It  is  evident  from  these  results  that  the  greatest  difficulty  in 
attaining  the  desired  degree  of  precision  is  in  the  determination 
of  the  rise  of  temperature  in  the  calorimeter.  For  a  rise  of  five 
degrees,  the  allowable  deviation  after  all  thermometric  and  radiation 
corrections  have  been  applied,  must  not  be  greater  than  0.013° 
and  this  cannot  be  attained  without  considerable  skill  and  care. 


60  NOTES  ON  PHYSICAL  LABORATORY  EXPERIMENTS 

To  measure  the  fall  in  temperature  of  the  substance  to  0.2° 
through  a  range  of  80°  necessitates  a  careful  determination  of  the 
correction  of  the  thermometer  used,  at  100°. 

On  the  other  hand  the  weight  of  the  substance  w  can  be  deter- 
mined with  ease  to  ten  times  the  required  precision  with  an  ordi- 
nary balance.  If  therefore  w  be  weighed  to  0.07  gram  or  even 
•  0.1  gram,  the  error  in  it  may  be  assumed  negligible,  and  hence 
the  allowable  deviations  in  the  temperature  measurements  may  be 
a  little  greater  without  increasing  the  deviation  of  the  final  result 
to  more  than  0.5  per  cent.  The  deviation  in  w0  +  k  may  also  be 
made  negligible  as  the  following  consideration  will  show. 


Suppose,  as  in  the  experiment,  that  the  specific  heat  of  all 
the  material  composing  the  calorimeter,  stirrer,  etc.  is  0.095  and 
that  its  total  weight  is  about  100  grams.  Then  k  =  9.5.  If  the 
value  0.095  is  reliable  to  a  per  cent,  i.e.,  about  one  unit  in  the 
third  decimal  place,  and  if  the  calorimeter  stirrer,  etc.,  be  weighed 
to  one  per  cent  or  better  0.5  per  cent,  i.e.,  the  nearest  half  gram, 
the  value  of  k  =  9.5  will  be  reliable  to  one  unit  in  the  tenths 
place.  Hence  if  the  water  be  weighed  to  the  nearest  0.1  gram  or 
0.2  gram  as  may  easily  be  done,  the  resulting  deviation  in  w0  +  k  = 
500  grams  will  not  be  more  than  1  or  2  parts  in  5000  and  hence 
negligible,  and  this  result  can  be  attained  without  materially  in- 
creasing the  difficulty  of  the  experimental  work.  Under  these 
conditions  the  function  can  be  treated  as  one  of  two  variables  and 
we  obtain  as  allowable  deviations  in  the  temperature  differences, 

l(U  —  ij)      a(fr  —  *i)      0.005 

=  u.ouoo, 


is  -  £2  fg  -  t\ 

from  which  if  ts  —  t2  =  80°  S(ts  —  t2)  =  0.29° 

and  tz  —  ti  =  5°  «(fc  —  *i)  =  0.16°. 

If  the  allowable  deviation  in  the  difference  of    two   quantities 
'2  —  *i  ig  &>  then  the  allowable  deviation  in  each  of  the  component 

• 
quantities  is  —.  —  .     Hence  the  allowable  deviation  in  each  reading 


,  . .„  ,      0.016° 

V^ 

0.29 


and  22  of  the  calorimeter  thermometer  will  be  ""~"   =  0.01 1°C. 


and  in  the  readings  ts  and  *2>  ~~7=  :=  °- 


LATENT    HEAT    OF   VAPORIZATION 

Problem. —  From  a  consideration  of  your  data  on  the  sub- 
stance investigated  and  the  above  precision  discussion,  calcu- 
late how  precise  the  following  quantities  should  be  deter- 
mined, in  order  to  ensure  an  accuracy  of  one  per  cent  in  the 
value  of  the  specific  heat: 

a,  the  rise  of  temperature  in  the  calorimeter ; 

b,  the  fall  of  temperature  of  the  substance  ; 

c,  the  weight  of  the  substance; 

d,  the  weight  of  water  in  the  calorimeter. 


LATENT    HEAT   OF   VAPORIZATION 

CONDENSATION   METHOD 

Object. —  The  object  of  this  experiment  is  to  determine  the 
latent  heat  of  vaporization  of  a  liquid  by  the  Condensation 
Method.  The  experiment  affords  an  excellent  example  of  a 
typical  calorimetric  measurement. 

Discussion. — When  a  substance  passes  at  constant  tempera- 
ture and  pressure  from  one  physical  state  to  another,  e.g.,  from 
solid  to  liquid,  or  liquid  to  vapor,  etc.,  a  certain  quantity  of 
heat  is  absorbed  or  evolved,  the  amount  of  which  correspond- 
ing to  the  transformation  of  one  gram  of  the  substance  in  ques- 
tion is  known  as  the  latent  heat  of  the  reaction.  Thus  if  the 
reaction  considered  is  the  change  of  one  gram  of  water  from 
the  liquid  to  the  vapor  state,  the  heat  required  to  affect  this 
change  under  the  above  conditions  is  called  the  latent  heat 
of  vaporization.  It  is  the  negative  of  the  latent  heat  of  con- 
densation, i.e.,  the  heat  evolved  when  one  gram  of  saturated 
vapor  condenses  to  one  gram  of  liquid  at  constant  pressure 
and  temperature.  The  latent  heat  of  any  reaction  consists  in 
general  of  two  parts,  one  corresponding  to  the  energy  involved 
in  the  molecular  changes  accompanying  a  change  of  physical 
state,  and  the  other  corresponding  to  the  external  work  which 
is  done  by,  or  on,  the  system  as  a  result  of  its  change  of  volume 
against  a  constant  pressure.  The  former  may  be  spoken  of 
as  the  change  in  the  internal  energy  of  the  substance  and  will 
be  denoted  by  e;  the  latter,  the  external  work,  is  given  by  the 


62      NOTES  ON  PHYSICAL  LABORATORY  EXPERIMENTS 

expression  p  (r2  -  vj  where  v2  and  vlf  are  the  specific  volumes 
of  the  substance  in  the  initial  and  final  states,  respectively. 
The  latent  heat  may  therefore  be  written 

.r  —  e  +  p(v2-v1). 

Of  the  terms  in  this  fundamental  expression,  only  r  can  be 
measured  directly;  e  itself  is  not  capable  of  direct  measure- 
ment; p  (ra  —  TI)  can  be  at  once  computed  when  the  pressure  p 
and  the  specific  volumes  r2  and  Vi  are  known.  Thus  in  the  case 
•of  the  vaporization  of  water  at  100°  C.,  and  under  atmospheric 
pressure,  760  mm.,  i\  =  1.043  r2  =  1661  cc.,  and  the  value  of 
the  external  work  in  calories  is  40.2.  The  total  number  of 
calories  r  required  to  vaporize  one  gram  of  water  under  these 
conditions  is  536.5,  hence  of  the  total  energy  required  to  vapor- 
ize the  water,  92.5  per  cent  is  expended  in  doing  internal  work 
and  7.5  per  cent  in  overcoming  the  atmospheric  pressure  during 
the  expansion. 

The  latent  heat  of  any  reaction  diminishes  with  rising  tem- 
perature, being  zero  at  the  critical  temperature  for  the  particu- 
lar change  of  state  considered.  From  Regnault's  data,  Clausius 
has  deduced  the  following  empirical  formula  for  the  latent  heat 
of  vaporization  of  water  between  the  temperatures  0°  C.  and 
200°  C., 

r  =  607  —  0.708*. 

If  the  latent  heat  of  vaporization  of  a  substance  is  multi- 
plied by  its  molecular  weight  m,  the  resulting  product  mr  =  A  is 
called  the  molecular  heat  of  vaporization.  Important  stochio- 
metrical  relations  have  been  found  to  hold  for  the  values  of  this 

quantity  for  different  liquids.     Thus  it  is  found  that  ™  =  const. 

for  a  large  class  of  analogous  liquids,  where  T  is  the  absolute 
boiling  temperature.  This  relation  is  known  as  Trouton's  law. 
The  numerical  value  of  the  constant  depends  on  whether  the 
molecular  weight  of  the  liquid  is  equal  to  or  greater  or  less  than 
that  of  its  vapor. 

The  most  important  methods  for  the  determination  of  the 
latent  heat  of  liquids  may  be  classified  as  follows: 

First. — The  Condensation  Method  in  which  the  quantity  of 


LATENT   HEAT   OF    VAPORIZATION 


63 


heat  given  out  by  the  condensation  of  a  measured  weight  of 
vapor  is  determined. 

Second. — The  Vaporization  Method  in  which  the  amount  of 
heat  absorbed  by  the  evaporation  of  a  measured  weight  of 
liquid  is  determined. 

Third. — The  Electrical  Method  in  which  the  quantity  of 
liquid  vaporized  at  its  boiling  point  by  heat  developed  elec- 
trically in  a  heating  coil  placed  within  the  liquid  is  measured. 

Apparatus. — The  apparatus  used  in  this  experiment  is  shown 
in  figure  13.  The  water  is  boiled  in  the  vessel  A  which  is 
closed  by  a  cover  setting  into  a  water  seal  B,  thus  preventing 


Fig.  13. 


the  escape  of  the  steam  at  the  top.  The  steam  passes  through 
a  small  tube  D  sealed  tangentially  into  the  cylinder  E,  a 
section  of  which  is  shown  in  figure  14.  It  circulates  with 
considerable  velocity  around  the  inside  of  E,  leaving  it  by 
means  of  the  central  tube  from  which  it  passes  on  to  the 
calorimeter.  The  object  of  this  device  is  to  deprive  the  steam 

of  any  moisture  which  it  may  carry 
mechanically.  This  is  deposited  on  the 
inner  wall  of  the  little  cylinder  and 
drops  back  into  the  water  through 
small  holes  in  the  bottom.  Unless 
the  sterm  is  "dry"  an  accurate  deter- 
minatirn  of  its  latent  heat  is  impossible. 


.  14. 


64      NOTES  ON  PHYSICAL  LABORATORY  EXPERIMENTS 

The  calorimeter  is  of  the  closed  type,  of  nickel-plated  cop- 
per, and  has  a  capacity  of  from  one  and  one-half  to  two  liters. 
It  is  shown  in  position  for  a  run,  resting  on  corks  inside  a 
water  jacket  J,  which  protects  it  from  outside  temperature 
changes.  In  the  centre  of  the  calorimeter  is  placed  the  con- 
densing coil  C  which  should  be  nearly  completely  immersed  in 
water.  In  the  base  of  the  condenser  is  a  bearing  for  the  stirrer 
which  is  mechanically  driven  by  means  of  a  small  electric  motor 
so  pivoted  at  X  that  it  can  be  swung  back  out  of  the  way,  or 
connected  with  the  stirrer,  as  desired. 

The  condenser  is  connected  with  the  boiler  by  means  of 
large  heavy  rubber  tubing  R  and  a  brass  elbow  F  lagged  with 
felt  to  prevent  condensation  of  the  steam.  The  brass  tube 
passing  through  the  stoppers  projects  well  up  into  F  so  as  to 
form  a  trap  for  collecting  any  water  which  may  become  con- 
densed before  the  steam  reaches  the  condenser.  The  steam 
should  enter  the  condenser  well  below  the  surface  of  the  water, 
otherwise  the  water  around  the  neck  of  the  coil  is  likely  to  be- 
come unduly  heated,  thus  causing  excessive  evaporation  and 
consequent  error  in  the  temperature  of  the  water  in  the  calo- 
rimeter. 

P  is  a  clamp  for  closing  the  rubber  connecting  tube,  and  S 
is  a  screen  for  protecting  the  calorimeter  from  the  heat  of  the 
burner  and  boiler. 

Procedure. —  Preliminary.  '  See  that  all  parts  of  the  appara- 
tus, water  jacket,  calorimeter,  coil,  stirrer  and  cover  have  the 
same  number.  Rinse  out  the  boiler  and  fill  it  with  about  two 
inches  of  clean  tap  water.  Fill  the  water  seal,  place  the  cover 
on  the  apparatus  and  allow  the  water  to  boil  some  time  so 
that  the  steam  may  warm  up  the  connecting  tubes  R  and  F 
before  the  experiment  proper.  In  the  mean  time  pour  out  any 
water  which  may  be  in  the  condenser  and  weigh  the  condenser 
to  centigrams.  The  exact  weight  of  the  coil  when  perfectly 
dry  is  given  with  the  apparatus  and  the  difference  between  this 
weight  and  the  weight  found  is  to  be  taken  as  so  much  addi- 
tional water  in  the  calorimeter.  Weigh  the  calorimeter,  cover, 
and  stirrer  together,  as  they  are  all  of  the  same  material,  to  the 


LATENT    HEAT    OF   VAPORIZATION  DO 

nearest  half  gram.  Next  place  the  coil  and  stirrer  in  the  calo- 
rimeter, fill  the  calorimeter  to  within  a  quarter  of  an  inch  of 
the  top  with  clean  tap  water,  put  on  the  cover,  and  weigh  all 
together  to  the  nearest  half  gram.  The  weight  of  water  can 
then  be  found  by  difference. 

Next  take  the  temperature  of  the  water  jacket,  which  should 
be  nearly  that  of  the  room  in  which  it  stands  continually.  In 
the  morning  it  will  often  be  found  below  this  temperature  owing 
to  the  fall  in  temperature  during  the  night.  In  this  case  it 
should  be  warmed  by  flashing  a  burner  on  the  outside  of  the 
jacket,  stirring  the  water  within  in  the  mean  time  by  blowing 
into  it  through  a  glass  tube.  In  this  experiment  the  rise  of 
temperature  is  at  a  uniform  rate  during  the  operation  and  hence 
the  Rumford  Method  of  correcting  for  radiation  is  applicable. 
As  the  temperature  is  to  be  allowed  to  rise  not  over  10°  or  12° 
C.,  the  initial  temperature  of  the  water  in  the  calorimeter 
should  be  adjusted  to  about  5°  or  6°  below  the  temperature  of 
the  jacket.  Under  no  circumstances  should  the  temperature  of 
the  calorimeter  be  so  low  that  moisture  precipitates  upon  it 
from  the  atmosphere.  The  outside  of  the  calorimeter  and  inside 
of  the  jacket  should  always  be  thoroughly  dry.  When  the  tem- 
perature is  adjusted  put  the  apparatus  together  as  in  the  figure. 
Before  connecting  'the  coil  with  the  boiler,  the  cover  should 
of  course  be  removed  from  the  latter  and  the  clamp  P  closed 
so  that  n<J  steam  can  enter  the  condenser  until  the  operation 
begins.  Before  connecting  F  to  the  coil  it  is  advisable  to  first 
remove  the  stopper  so  as  to  release  any  water  collected  in  the 
trap,  otherwise  it  is  likely  to  fill  up  during  the  operation  and  run 
over  into  the  condenser.  See  that  there  is  plenty  of  water  in 
the  boiler,  and  in  the  water  seal  before  beginning  the  experi- 
ment proper,  so  that  no  further  attention  need  be  paid  to  these 
during  or  before  the  operation  of  passing  steam  into  the  coil. 
The  water  should  be  allowed  to  boil  continually.  The  stirrer 
should  be  set  in  action  several  minutes  before  beginning  to 
record  temperatures. 

Prepare  a  sheet  for  recording  data  in  two  columns,  one  for 
times  (half  minute  intervals — whir1  should  be  written  down 
beforehand),  and  one  for  temperatr  :>s. 


66      NOTES  ON  PHYSICAL  LABORATORY  EXPERIMENTS 

Experiment  Proper.  —  The  temperature  readings  are  to  be 
taken  without  interruption  every  half  minute  throughout  the 
whole  experiment. 

First.  —  Take  preliminary  half-minute  temperature  readings 
of  the  calorimeter  for  six  to  eight  minutes. 

Second.  —  Open  P,  put  on  the  cover  of  the  boiler  and  note 
the  instant  when  the  temperature  begins  to  rise  suddenly. 
Continue  reading  the  temperature  of  the  calorimeter  every 
half  minute  until  the  temperature  has  risen  10°  or  12°  C. 

Third.  —  Take  off  the  cover,  close  P  and  continue  taking 
temperatures  for  six  to  eight  minutes  longer. 

Fourth.  —  Remove  the  coil,  dry  the  outside  very  carefully, 
and  weigh  as  soon  as  possible  to  centigrams. 

Fifth.  —  Record  the  reading  of  the  barometer  and  its  attached 
thermometer. 

Computation.  —  Make  a  plot  of  the  time  and  temperature  ob- 
servations and  determine  the  corrected  final  temperature  t% 
of  the  calorimeter  by  special  method  I  or  II  (pp.  52-54);  find 
from  proper  tables,  the  temperature  ts  of  the  steam  under  the 
reduced  barometric  pressure  at  the  time  of  the  experiment. 
Let  r  =  latent  heat; 

wc  =  weight  of  the  condenser  dry; 
w  =  weight  of  water  condensed  in  the  coil; 
w0  =  weight  of  water  in  calorimeter; 
MI  +  W2  +  wz  =  weight  of  calorimeter,  cover  and  stirrer; 

£j  =  corrected  initial  temperature  of  calorimeter; 
/2  =  corrected  final  temperature  of  calorimeter; 
ts  =  corrected  temperature  of  steam; 

sc,  §!,  sa,  s3  =  specific  heat  of  the  condenser  and  parts  of  calo- 
rimeter, respectively.  '  These  may  all  be  assumed  equal  to  0.095. 
The  heat  given  out  by  the  steam  in  condensing  to  water  at 
ts°  plus  the  heat  given  out  by  this  water  in  cooling  to  t%°  is  equal 
to  the  quantity  of  heat  corresponding  to  the  rise  of  temperature 
of  the  calorimeter  and  its  contents,  that  is 

rw  +  w  (t,  —  y  =  (w0  +  k)  (^  —  y, 


from  which  r  = 

w 


MECHANICAL    EQUIVALENT    OF   HEAT  — I  67 

where  k  is  the  water  equivalent  of  the  calorimeter,  cover,  stirrer, 
and  condenser,  i.e., 

k  =  wcsc  +  uy?i  +  wfa  +  W3s3 
=  0.095  (wc  +  w1  +w2  +  wj. 

Problem. — From  a  consideration  of  the  magnitude  of  the 
quantities  measured  in  this  experiment,  calculate  approxi- 
mately how  precise  the  following  quantities  should  be  deter- 
mined in  order  to  attain  a  precision  of  one-half  of  one  per 
cent  in  the  final  value  of  the  latent  heat: 

a.  Rise  of  temperature  in  calorimeter; 

b.  Fall  of  temperature  of  condensed  steam; 

c.  Weight  of  condensed  water; 

d.  Value  of  total  water  equivalent  (w0  +  fc)  of  the  calorim- 

eter and  contents. 


MECHANICAL    EQUIVALENT    OF    HEAT  — I 

Object. — The  object  of  this  experiment  is  to  determine  the 
value  of  the  mechanical  equivalent  of  heat  by  the  electrical 
method.  The  experiment  furnishes  further  practice  in  calo- 
rimetry  and  in  the  measurement  of  quantities  of  energy.  A 
study  of  the  electrical  apparatus  employed  is  also  very  instruc- 
tive as  illustrating  the  transformation  of  high  potential  direct 
currents  to  direct  currents  of  low  potential. 

Discussion. — The  mechanical  equivalent  of  heat  is  the  value 
of  one  calorie  expressed  in  ergs,  that  is,  the  factor  for  reducing 
heat  energy  expressed  in  calories  to  mechanical  energy  ex- 
pressed in  ergs.  Until  recently  all  exact  determinations  of  this 
quantity,  Joule's,  Rowland's,  and  others,  consisted  essentially 
in  measuring  the  quantity  of  mechanical  energy  transformed 
by  some  device  directly  into  heat  energy,  the  amount  of  which 
was  measured  calorimetrically.  If  a  ergs  are  found  to  pro- 
duce b  calories,  by  the  principle  of  the  conservation  of  energy, 
these  two  quantities  of  energy  must  be  equal,  i.e.,  a  ergs=.& 

calories,  and  the  factor  J  =  -  is  therefore  the  desired  factor 
for  reducing  calories  to  ergs. 


68     NOTES  ON  PHYSICAL  LABORATORY  EXPERIMENTS 

The  same  result  may  be  equally  well  obtained  if  some  other 
form  of  energy,  e.g.,  electrical  energy  be  transformed  into  heat, 
provided,  first,  that  the  relation  of  the  units  in  which  it  is  meas- 
ured to  the  erg  is  exactly  known,  and  second,  that  electrical 
energy  can  be  measured  with  the  same  degree  of  accuracy  as 
mechanical  energy.  With  the  refined  methods  and  instruments 
of  electrical  measurement  at  our  disposal,  this  is  now  possible, 
as  recent  determinations  of  the  mechanical  equivalent  by  wholly 
•electrical  means  have  shown.1 

The  determination  of  this  fundamental  physical  constant 
with  a  high  degree  of  accuracy  requires  elaborate  apparatus 
and  very  careful  manipulation.  An  accuracy  of  half  of  one 
per  cent  may  be  obtained,  however,  without  much  difficulty. 

The  method  consists  in  measuring  the  electrical  energy  ex- 
pended in  heating  a  coil  of  wire  placed  in  a  calorimeter,  on  the 
one  hand,  and  the  heat  energy  thereby  resulting,  on  the  other. 
As  the  heating  effect  of  a  current  is  given  by  the  expression 
Q  =  lEt  or  Q  =  PRt  the  electrical  input  may  be  obtained  by 
measurements  either  of  current,  voltage,  and  time,  or  cur- 
rent, resistance,  and  time.  The  former  method  is  the  more 
convenient  and  direct,  as  by  it  we  measure  the  two  factors 
which  primarily  constitute  electrical  energy,  namely,  potential 
and  quantity  of  electricity  (current  X  time).  Moreover  both 
of  the  quantities  /  and  E  can  be  determined  with  an  accuracy 
of  0.1  or  0.2  per  cent,  by  direct-reading  instruments.  The 
measurement  of  the  heat  energy  is  made  in  the  usual  way,  all 
precautions  necessary  to  accurate  calorimetric  measurements 
being  observed.  A  precision  of  two  or  three  tenths  of  a  per  cent 
can  be  obtained  without  serious  difficulty. 

Apparatus. — The  apparatus  consists  of'  a  closed  calorimeter 
resting  on  cork  supports  inside  a  water  jacket.  The  heating 
coil  of  flattened  manganine  wire  fits  concentrically  inside  the 
calorimeter.  Manganine  is  employed  on  account  of  its  very 
low  temperature  coefficient,  and  the  wire  is  flattened  so  as  to 
:give  a  greater  radiating  surface.  Inside  the  coil  and  supported 
by  the  frame  is  the  stirrer,  carrying  two  sets  of  vanes,  which, 

i Griffith,  "Determination  of  Mech.  Equiv.  of  Heat,"  Phil.  Trans.,  184,  p.  361, .1893. 


MECHANICAL  EQUIVALENT  OF  HEAT — I          69 

when  rapidly  rotated  by  a  small  hot-air  engine,  keeps  the  water 
in  violent  agitation.  The  brass  terminals  of  the  coil  project 
through  insulated  holes  in  the  cover,  and  can,  after  the  calo- 
rimeter, coil  and  cover  are  in  place,  be  easily  connected  by 
flexible  leads  to  the  source  of  current. 

The  current  is  furnished  by  a  motor-generator  running  on 
the  220  volt  circuit  and  delivering  energy  at  12  volts.  A  low 
voltage  is  desirable  in  this  experiment  to  avoid  electrolysis. 
By  means  of  a  heavy  fly  wheel  and  the  device  of  "floating"  a 
set  of  batteries  across  the  terminals  of  the  heating  coil,  fluctu- 
ations arising  from  variations  in  the  impressed  voltage  can 
be  almost  wholly  eliminated.  The  generator  is  to  be  started 
by  an  instructor  who  will  explain  further  details.  A  storage 
battery  of  large  capacity  is  also  very  well  suited  for  furnishing 
electrical  energy  for  this  experiment. 

The  current  is  measured  by  a  Weston  ammeter  which  is  con- 
nected in  series  with  the  heating  coil.  The  potential  at  the 
terminals  of  the  heating  coil  is  measured  by  a  Weston  volt- 
meter connected  by  potential  leads  to  these  points.  The  cir- 
cuit is  made  and  broken  by  a  knife  switch. 

Procedure. —  Two  students  will  be  assigned  together  to  this 
experiment.  Data  should  be  recorded  on  blanks  made  out 
before  the  exercise,  similar  to  those  in  the  sample  notebook. 

Preliminary. — Weigh  the  calorimeter,  cover,  and  coil  dry. 
The  weights  and  specific  heats  of  the  individual  parts  of  the 
heating  coil  are  given  with  the  apparatus.  Place  the  coil  in  the 
calorimeter  and  fill  the  latter  with  cold  tap  water  so  that  the 
coil  and  frame  are  completely  immersed,  and  weigh.  The  tem- 
perature of  the  water  should  be  at  least  three  or  four  degrees 
below  that  of  the  water  in  the  jacket. 

Set  up  the  apparatus  for  a  run.  Start  the  hot  air  engine  and 
stirrer.  After  the  latter  has  been  in  action  some  minutes  note 
the  temperature  of  the  calorimeter,  and  also  that  of  the  inside 
of  the  outer  water  jacket;  the  latter  should  be  at  about  room 
temperature,  and  several  degrees  above  that  of  the  water  in 
the  calorimeter.  Since  in  this  experiment  the  rate  at  which 
heat  is  put  into  the  calorimeter  is  practically  uniform  from 


70  NOTES   ON   PHYSICAL   LABORATORY  EXPERIMENTS 

start  to  finish,  the  Rumford  method  of  eliminating  the  radi- 
ation correction  may  be  advantageously  employed.  The  rise 
of  temperature  in  the  calorimeter  should  be  about  five  degrees; 
the  initial  temperature  of  the  calorimeter  should  therefore  be 
brought  up  to  within  2.5°  of  that  of  the  surroundings.  This 
can  be  done  exactly  by  closing  the  circuit  for  a  few  minutes 
and  allowing  the  current  to  heat  up  the  water  in  the  calorim- 
eter by  the  proper  amount.  The  circuit  should  never  under  any 
circumstances  be  closed  unless  the  heating  coil  is  wholly  immersed 
in  water.  The  apparatus  and  connections  should  be  inspected 
by  an  instructor  before  the  circuit  is  closed. 

Experiment  proper. — Having  adjusted  the  initial  tempera- 
ture of  the  water  in  the  calorimeter,  all  is  ready  for  the  run. 
One  student  A,  is  to  open  and  close  the  circuit  and  read  the 
voltmeter  and  ammeter;  the  other  B,  is  to  read  the  thermometer. 
Each  should  prepare  blanks  beforehand  for  recording  his  ob- 
servations. Temperatures  are  to  be  taken  every  half  minute, 
and  voltmeter  and  ammeter  readings  alternately  every  fifteen 
seconds.  A  preliminary  series  of  temperature  readings  are  to 
be  taken  for  five  minutes  before  closing  the  circuit;  then  at  a 
noted  instant,  preferably  on  the  minute,  the  circuit  is  closed, 
and  voltmeter  and  ammeter  read  instantly.  When  the  tem- 
perature has  risen  nearly  five  degrees,  B,  reading  temperatures, 
should  notify  A,  who,  at  a  noted  instant,  opens  the  switch.  The 
switch  should  be  opened  and  closed  as  nearly  at  the  noted  times 
as  possible,  so  as  to  reduce  the  error  in  the  time  measurement 
to  a  minimum.  The  temperature  of  the  calorimeter  should  be 
continuously  observed  five  minutes  longer  to  provide  all  neces- 
sary data  for  correcting  for  radiation  and  mechanical  heating 
due  to  stirring,  if  these  be  not  wholly  eliminated  by  the  above- 
described  method  of  procedure.  This  completes  one  set  of  data. 

The  water  in  the  calorimeter  should  then  be  cooled  to  a  tem- 
perature below  that  of  its  surroundings  and  a  duplicate  run  made 
in  exactly  the  same  manner,  A  and  B  changing  places. 

Computation. —  The  calorimetric  data  are  to  be  plotted  and 
the  corrected  rise  of  temperature  determined  as  described  under 
special  case,  I  or  II,  pp.  52-54.  The  computation  of  the  elec- 


MECHANICAL   EQUIVALENT  OF  HE./VT — I  71 

trical  energy  is  to  be  made  as  follows:  Since  all  ammeter  and 
voltmeter  readings  are  taken  at  equal  time  intervals,  the 
mean  voltage  and  current  multiplied  by  the  total  time  may 
be  taken  without  error  for  the  sum  of  the  products  of  each  pair 
of  readings  multiplied  by  the  corresponding  time  interval.  The 
mean  value  of  the  current  and  voltage  must  be  corrected  for 
instrumental  errors.  The  calibration  corrections  of  the  in- 
struments used  will  be  found  with  the  instruments.  The  "zero 
error"  should  be  observed  by  the  student.  Without  careful 
calibration,  the  instruments  cannot  be  assumed  correct  to 
0.1-0.2  per  cent. 

The  product,  current  (in  amperes)  X  potential  (in  volts)  X 
time  (in  seconds)  gives  the  total  electrical  energy  expended  in 
heating  the  calorimeter,  expressed  in  joules.  Equating  this 
quantity  to  the  number  of  calories  actually  measured,  the  value 
of  one  calorie  expressed  in  the  practical  unit  of  electrical  energy, 
the  joule  is  readily  obtained.  To  reduce  this  value  to  the  ab- 
solute unit  of  energy,  the  erg,  we  must  know  the  value  of  a 
joule  in  ergs.  The  system  of  electrical  units  is  so  defined  that 
one  joule  =  107  ergs. 

Each  student  is  to  compute  one  run  independently,  but  the 
final  results  of  both  are  to  be  handed  in  for  comparison. 

Problems. — How  many  joules  are  necessary  to  vaporize 
100  grams  of  water  at  its  boiling  point  under  standard  condi- 
tions of  pressure?  If  this  energy  is  supplied  at  the  rate  of  100 
watts,  what  time  will  be  necessary?  If  the  resistance  of  the 
coil  is  10  ohms,  what  current  and  voltage  will  be  necessary? 
With  a  110- volt  pircuit  what  must  /  and  R  be? 

2.  What  must  be  the  percentage  precision  of  /,  E,  and  t  in 
order  that  the  resultant  deviation  in  Q  is  not  greater  than  0.5 
per  cent? 

3.  What  are  the  allowable  deviations  in  amperes,  volts,  and 
seconds  corresponding  to  the  precision  prescribed  in  problem  2 
if  the  value  of  /,  E,  and  t  are  the  mean  values  found  in  the  ex- 
periment?    Do  you  think  this  degree  of  precision  was  attained? 


72  NOTES  ON    PHYSICAL    LABORATORY    EXPERIMENTS 


MECHANICAL    EQUIVALENT    OF    HEAT  —  II 

CONTINUOUS    CALORIMETER 

Object. —  The  object  of  this  experiment  is  to  give  prac- 
tice in  the  use  of  a  continuous  calorimeter  for  measuring 
heat  energy.  The  method  is  illustrated  by  a  determina- 
tion of  the  mechanical  equivalent  of  heat  by  the  electrical 
•method. 

Discussion. —  The  principle  of  a  continuous  calorimeter  is  as 
follows:  Heat  is  generated  at  a  uniform  rate  within  a  calo- 
rimeter which  is  so  constructed  that  the  heat  can  escape  only 
by  conduction  and  radiation  through  a  stream  of  water  which 
circulates  through  the  apparatus.  The  temperature  of  the  in- 
coming water  must  be  below  the  temperature  of  the  room 
(surroundings);  its  rate  of  circulation  through  the  calorim- 
eter is  so  regulated  that  its  temperature  when  it  leaves  the 
apparatus  has  been  raised  just  to  the  temperature  of  the 
room.  Under  these  circumstances  the  outflowing  water  con- 
ducts away,  at  a  constant  rate,  the  heat  generated  within  the 
calorimeter,  and  the  amount  of  heat  generated  in  a  given  time 
will  be  measured  by  the  quantity  of  water  flowing  in  that  time, 
multiplied  by  the  rise  of  temperature  which  the  water  has 
experienced  in  passing  through  the  apparatus.  A  determina- 
tion of  the  difference  in  temperature  of  the  incoming  and  out- 
going water  when  a  state  of  equilibrium  has  been  established 
in  the  calorimeter,  and  of  the  quantity  of  water  flowing  through 
in  a  given  time,  furnishes  therefore  all  'data  necessary  for 
computing  the  rate  of  heat  development  within  the  calorim- 
eter. 

A  little  consideration  will  show  that,  in  order  that  a  state  of 
thermal  equilibrium  may  be  established  within  the  apparatus 
the  following  conditions  must  be  fulfilled: — 

(a)  The  heat  must  be  generated  uniformly. 
(6)  The  water  must  flow  uniformly,  i.e.,  under  a  constant 
pressure. 


1    UNIY-.-.SITV 

V  °r       \S 

MECHANICAL  EQUIVALENT    G^^Ji^^^^  73 

(c)  The   temperature  of  the  incoming  water  must  be  con- 

stant. 

(d)  The  temperature  of  the  surroundings  must  be  constant. 

Under  these  conditions  it  is  to  be  particularly  noted  that  the 
usual  correction  for  radiation,  so  troublesome  in  most  calori- 
metric  experiments,  may  be  entirely  eliminated,  for,  if  the  out- 
going water  is  caused  to  circulate  within  the  outside  wall  of 

the  calorimeter,  and  its  temperature 
is  maintained  the  same  as  the  tem- 
perature of  the  surrounding  air,  there 
will  be  no  exchange  of  heat  by  the 
apparatus  either  by  radiation  or  con- 
duction to  or  from  the  surroundings, 
no  matter  what  may  be  the  duration 
of  the  experiment. 

The  apparatus  described  below  is 
designed  to  meet  the  above  require- 
ments, and  to  give  the  calorimetric 
results  reliable  to  at  least  0.5  per 
cent. 

Apparatus. —  The  general  arrange- 
ment of  the  apparatus  is  shown  in 
Fig.  15.  The  water  is  piped  directly 
from  the  street  mains,  in  order  to  in- 
sure a  constant  temperature  below 
that  of  the  laboratory,  into  an  over- 
flow tank  A,  placed  about  ten  feet 
above  the  apparatus,  which  furnishes 
a  supply  at  a  constant  pressure.  The  water  from  the  tank 
flows  down  into  the  calorimeter  at  B,  circulating  up  and 
down  around  an  enclosed  heating  coil,  as  shown  in  Fig.  16, 
and  finally  leaves  it  at  C.  D  is  a  three-way  cock,  by  means 
of  which  the  water  can  be  run  off  into  the  waste  pipe  E,  or 
collected  through  F.  The  temperature  of  the  incoming  water 
is  taken  by  the  thermometer  inserted  at  B,  and  of  the  outgoing 
water  at  C. 


Fig.  15. 


74 


NOTES  ON  PHYSICAL  LABORATORY  EXPERIMENTS 


The  details  of  the  calorimeter  are  shown  in  Fig.  16.  It 
consists  of  a  small  inner  brass  tube  around  which,  but  insu- 
lated from  it,  are  wound  a  number  of  turns  of  fine  ger- 

man-silver  wire.  In  order 
to  insulate  the  wire  and 
also  to  facilitate  the  con- 
duction of  the  heat  gen- 
erated in  it  to  the  water, 
the  coil  is  completely  im- 
mersed in  oil. 

The  incoming  water 
passes  down  through  the 
heating  coil  and  then  circu- 
lates up  and  down  through 
the  calorimeter  as  shown  in 
the  figure.  A  pinch-cock 
regulates  the  flow  at  P.  A 
small  reservoir  R,  con- 
nected to  the  oil-jacket, 
serves  to  receive  the  over- 
flow due  to  the  expansion 
of  the  oil  when  heated  by 
the  current  in  the  coil. 

The  calorimeter  is  placed 
inside  a  metal  jacket  to 
protect  it  from  draughts. 
Both  calorimeter  and 
jacket  are  nickel-plated 

and  highly  polished  to  diminish  the  radiation.  A  vessel  for 
collecting  the  water  and  suitable  scales  for  weighing  it  are 
provided. 

The  electrical  measuring  instruments  required  consist  of  a 
portable  Weston  ammeter  and  volt-meter,  the  former  being 
connected  in  series  with  the  heating  coil,  and  the  latter  across  its 
terminals.  The  coil  is  connected  directly  to  the  110-volt  mains. 
The  instruments  are  calibrated  and  their  corrections  will  be 
found  on  them. 


Fig.  16. 


MECHANICAL   EQUIVALENT   OF   HEAT  —  II  75 

Procedure. —  This  experiment  is  to  be  performed  by  two  stu- 
dents working  together.  Data  should  be  recorded  similar  to 
those  in  the  sample  note-book.  All  pipe  and  electrical  connec- 
tions should  be  explained  by  an  instructor  before  the  experi- 
ment is  begun. 

Preliminary. — Allow  the  water  to  flow  through  the  apparatus 
with  the  pinch-cock  P,  which  regulates  the  outflow  of  the  water 
from  the  calorimeter,  wide  open  so  that  a  full  stream  runs 
through  the  calorimeter  into  the  waste  pipe  E.  Close  the  cir- 
cuit containing  the  heating  coil. 

When  the  temperature  of  the  inflowing  water  has  become 
constant  to  0.2°  for  at  least  two  minutes,  begin  regulating  the 
outflow  by  the  pinch-cock  P  so  that  its  temperature  approaches 
that  of  the  room.  While  waiting  for  the  outflowing  water  to 
come  to  a  constant  temperature,  weigh  the  vessel  for  collecting 
the  water  and  arrange  the  blanks  for  recording  the  observations. 

When  the  outflowing  water  has  come  to  a  constant  temper- 
ature, note  whether  it  is  above  or  below  that  of  the  surroundings, 
i.e.,  the  temperature  of  the  air  just  inside  the  calorimeter  jacket. 
If  above,  open  the  pinch-cock  slightly  to  allow  the  water  to  flow 
more  rapidly,  and  wait  until  the  temperature  again  becomes  con- 
stant. If  below,  close  the  pinch-cock  slightly,  and  wait  as  be- 
fore. A  fraction  of  a  revolution  of  the  pinch-cock  screw  will 
be  found  to  produce  a  considerable  variation  in  the  ultimate 
temperature  of  the  outgoing  water.  When  the  stationary  con- 
dition of  temperature  is  reached,  the  temperature  of  the  out- 
going water  should  not  vary  more  than  0°.l  in  three  minutes. 
Continue  this  operation  (being  sure  to  wait  long  enough  after 
each  adjustment  for  equilibrium  to  be  established)  until  the 
temperature  of  the  outgoing  water  is  within  0°.2  of  that  of  the 
surroundings.  When  this  condition  is  reached,  but  not  before, 
begin  the  experiment  proper. 

Experiment  proper. — One  student  will  give  the  signals  and 
note  the  times  of  starting  and  stopping  the  run,  and  will  record 
readings  alternately  of  the  voltmeter  and  ammeter  every  fif- 
teen seconds  for  ten  minutes.  The  other  student  will  begin  to 
collect  and  stop  collecting  the  water  at  the  signals- given,  weigh 


76     NOTES  ON  PHYSICAL  LABORATORY  EXPERIMENTS 

the  water,  and  record  the  temperatures  of  the  ingoing  and  out- 
coming  water  alternately  at  intervals  of  fifteen  seconds  during 
the  run.  The  temperature  of  the  surroundings  should  also  be 
recorded  at  the  beginning,  middle,  and  end  of  the  run. 

A  short  time,  half  a  minute  or  so,  before  beginning  the  run, 
turn  the  three-way  cock  so  that  the  water  will  flow  out  through 
F  into  any  convenient  vessel.  Then  at  the  signal  for  starting 
the  run,  begin  to  collect  the  water  for  weighing  by  quickly 
placing  an  appropriate  vessel  of  four  litres  or  more  capacity 
under  F.  This  procedure  for  collecting  the  water  has  been 
found  to  introduce  less  initial  error  than  turning  the  three-way 
cock  from  E  to  F  at  the  starting  signal.  At  once  begin  to  read 
the  temperatures  of  the  incoming  and  outgoing  water.  At  the 
signal  for  concluding  the  run  (duration  about  ten  minutes), 
stop  collecting  the  water  by  pinching  the  end  of  the  rubber  tube 
with  the  fingers,  and  at  once  turn  the  three-way  cock  so  that  the 
water  will  again  flow  into  the  waste  pipe  E.  Weigh  the  quan- 
tity of  water  collected. 

This  completes  one  set  of  data.  The  run  should  be  repeated, 
the  two  observers  changing  places. 

Computation. — The  electrical  input  is  to  be  computed  from  the 
mean  ammeter  and  voltmeter  readings  corrected  for  zero  and 
calibration  errors,  and  the  time.  The  corresponding  value  of 
the  heat  energy  evolved  is  to  be  computed  from  the  mean  differ- 
ence of  temperature  of  the  incoming  and  outgoing  water  and 
its  weight.  If  the  temperature  readings  are  nearly  constant, 
as  they  should  be,  the  difference'  of  the  mean  temperature  of 
the  incoming  and  outgoing  water  may  be  used  in  the  compu- 
tation. The  thermometers  used  must  be  very  carefully  compared 
with  each  other.  The  corrections  are  given. 

Each  student  is  to  compute  one  run  independently,  but  the 
final  results  of  both  are  to  be  handed  in  for  comparison.  The 
problems  on  page  71  should  also  be  included  unless  previously 
handed  in. 


EXPANSION 


The  determination  of  the  coefficients  of  expansion  of  liquids, 
solids,  or  gases  with  any  high  degree  of  precision  requires  skill- 
ful manipulation  and  attention  to  numerous  details  and  cor- 
rections, and  not  infrequently  the  use  of  least  squares  in  the 
reduction  of  the  data.  Special  apparatus  including  compara- 
tors, and  Abbe's  Dilatometer  (Fizeau's  apparatus),  is  provided 
for  this  work,  which  is  offered  to  students  who  are  qualified  to 
undertake  it.  The  work  is  not  required  however  in  the  in- 
troductory laboratory  course. 


APPENDIX 


The  data  in  the  following  abbreviated  tables  are  taken  from  Landolt  and 
Bornstein's  "  Physikalisch-chemische  Tabellen." 


B  TABLE  I. 
LINEAR  COEFFICIENTS  OF  EXPANSION. 


Aluminium  . 

0.000023 

Lead       .            .            .    . 

0.000029 

Brass     

0.000019 

Platinum  .    .             ... 

0.000009 

Copper  

0.000017 

Platinum-ir  id  ium 

0.000009 

German  Silver     
Glass  ordinary 

0.000018 
0  0000085 

Silver     
Tin 

0.000019 
0  000023 

Gold 

0  000015 

Vulcanite 

0  00008 

Iron   . 

0  000012 

Zinc    . 

0  000029 

Wood  with  the  grain 0.000003  to  0.000010 

Wood  across  the  grain 0.000033  to  0.000061 


TABLE   II 
MEAN  CUBICAL  COEFFICIENTS  OF  EXPANSION  BETWEEN  0°  AND  100°. 


Benzene 

0  00138 

Mercury 

0  000181 

Toluene 

0  00121 

Ether 

000215 

Turpentine 

0.00105 

Alcohol 

0  00104 

Chloroform  

0.00140 

0  000534 

For  water,  Vt  =  V0  (l  +  at  +  bt*  + 
where  a  =  —  0.00006581. 
6  =  +  0.00000851. 
C  =  —  0.000000068. 
v0  =  volume  at  0°  C. 
vt  =  volume  at  t°  C. 


APPENDIX 


TABLE  III. 
MEAN  COEFFICIENTS  OF  EXPANSION  OF  GASES  BETWEEN  0°  A^D  100°. 


Volume  Constant. 

Pressure  Constant. 

Air     .    .    »   «    

0.003669 

0.003671 

Oxygen 

0.003674 

Hydrogen 

0.003668 

0  003661 

Nitrogen                    

0.003668 

Carbonic  Oxide     

0.003667 

0.003669 

Carbonic  Acid  

0.003706 

0.003710 

Nitrous  Oxide  

0.003676 

0.003720 

TABLE  IV. 
MELTING  POINTS  (HOLBORN  &  DAY,  1901). 


Cadmium 

321  °7  ±  0  °1  (From  10  observations  on  two  days.) 

Lead 

326°9dbO°2        "      "             "               "      "        " 

Zinc    
Antimony  
Aluminium    
Silver      
Silver     
Gold    
Copper 

419.9   ±0.2 
630.5   ±0.3 
657.5  ±0.5    (In  a  graphite  crucible,  a  lower  value. 
961.5  ±0.9    (Pure  ;  i.e.,  in  a  reducing  atmosphere. 
955                (In  air;  point  ill  denned.) 
1064 
1065               (In  air  ) 

Copper    

1084.              (Pure.) 

TABLE   V. 
BOILING  POINTS  OF  LIQUIDS  AT  760  mm.  PRESSURE. 


Water   .    ;    

100  °C. 

Benzene     

80.°0 

Mercury 

357  03 

Glycerine 

290  °0 

Sulphur 

444  °0 

Alcohol  

78  °2 

Naphthaline     .    .    .    .    ..   . 
Toluene 

218.°0 
110  °0 

Turpentine    
Chloroform 

159.°0 
61  °2 

80 


APPENDIX 


TABLE   VI. 
LATENT  HEATS  OF  VAPORIZATION  EXPRESSED  IN  O°  CALORIES. 


Temperature  of 
Vaporization. 

Latent  Heat. 

350 

62  00 

Alcohol 

78 

206  4 

Ether      .    .    .    . 

34.9 

89.96 

Toluene                                       ...... 

110.8 

83.55 

Turpentine             •                         

159.3 

74.04 

Ammonia                    

7.8 

294.2 

Benzene     .            .        

80.1 

92.91 

Water 

100 

536  2  (15°  to  16°) 

Clausius's  formula  for  the  variation  of  the  latent  heat  of  vaporization  of  water 
with  the  temperature  is,  r  =  607  —  .7Q8t  when  t  is  the  temperature  of  vaporization  in 
degrees  centigrade. 


TABLE  VII. 
SPECIFIC  HEATS  OF  VARIOUS  LIQUIDS  AND  SOLIDS. 


Alcohol  at  17°  

0.58 

Glass     between  15-100°  .    . 

0.20 

Aniline  "    "  

0.49 

Gold                         "   . 

0.032 

Benzene  "    "  

0.36 

Iron                            "... 

0.113 

Mercury  "    "  

0.034 

Lead           "             "... 

0.032 

Toluene  "    " 

0.40 

Nickel        "             *'   . 

0.11 

Turpentine  at  17°    .            .    . 

0.43 

Platinum    "             "... 

0.033 

Aluminium  between  15-100°  . 

0.218 

Quartz        "             "... 

0.191 

Brass                   "             " 

0.093 

Silver         "             "... 

0.057 

Fluorspar                          " 

0.208 

Tin              "             "... 

0.056 

Copper                              " 

0.093 

Zinc                           M  .    .    . 

0.094 

APPENDIX 


81 


TABLE  VIII. 

TEMPERATURE,  PRESSURE,  AND  SPECIFIC  VOLUME  OF  SATURATED 

VAPOR.i 


Temperature 
in  Degrees 
Centigrade. 

Pressure  in 
mm.  of 
Mercury. 

O  ®  rn 

ail 

§£  § 

%>a 

Temperature 
in  Degrees 
Centigrade. 

Pressure  in 
mm.  of 
Mercury. 

Specific 
Volume 
in  c.cm. 

Temperature 
in  Degrees 
Centigrade. 

Pressure  in 
mm.  of 
Mercury. 

«  ®  rt 

||| 

£>  B 

0 

4.602 

211500 

38 

49.308 

21860 

76 

300.83 

3965 

l 

4.941 

197700 

39 

52.05 

20770 

77 

313.59 

3813 

2 

5.303 

184600 

40 

54.91 

19740 

78 

326.80 

3668 

3 

5.689 

172400 

41 

57.92 

18760 

79 

340.48 

3529 

4 

6.100 

161200 

42 

61.06 

17840 

80 

354.63 

3397 

5 

6.536 

150800 

43 

64.35 

16980 

81 

369.27 

3270 

6 

7.001 

141200 

44 

67.80 

16160 

82 

384.41 

3149 

7 

7.494 

132200 

45 

71.40 

15390 

83 

400.08 

3033 

8 

8.019 

123900 

46 

75.16 

14660 

84 

416.27 

2922 

9 

8.576 

116200 

47 

79.10 

13970 

85 

433.01 

2815 

10 

9.167 

109000 

48 

83.21 

13310 

86 

450.31 

2714 

11 

9.795 

102300 

49 

87.51 

12690 

87 

468.18 

2616 

12 

10.460 

96090 

50 

91.98 

12110 

88 

486.64 

2523 

13 

11.164 

90190 

51 

96.65 

11560 

89 

505.71 

2433 

14 

11.911 

84760 

52 

101.54 

11030 

90 

525.40 

2347 

15 

12.702 

79690 

53 

106.64 

10530 

91 

545.72 

2265 

16 

13.539 

74970 

54 

111.95 

10060 

92 

566.70 

2186 

17 

14.423 

70560 

55 

117.49 

9610 

93 

588.34 

2110 

•  18 

15.360 

66440 

56 

123.25 

9185 

94 

610.67 

2038 

19 

16.349 

62580 

57 

129.26 

8782 

95 

633.70 

1968 

20 

17.395 

58980 

58 

135.51 

8399 

96 

657.45 

1901 

21 

18.498 

55610 

59 

142.02 

8036 

97 

681.93 

1836 

22 

19.663 

52460 

60 

148.80 

7687 

98 

707.17 

1774 

23 

20.892 

49510 

61 

155.85 

7362 

99 

733.19 

1715 

24 

22.188 

46740 

62 

163.18 

7051 

100 

760.00 

1661 

25  ' 

23.554 

44150 

63 

170.80 

6754 

101 

787.5 

1609 

26 

24.994 

41720 

64 

178.72 

6470 

102 

815.8 

1556 

27 

26.510 

39450 

65 

186.95 

6201 

103 

845.0 

1505 

28 

28.107 

37310 

66 

195.50 

5947 

104 

875.1 

1456 

29 

29.786 

35300 

67 

204.38 

5705 

105 

906.0 

1409 

30 

31.553 

33420 

68 

213.60 

5472 

106 

937.9 

1365 

31 

33.411 

31650 

69 

223.17 

5250 

107 

970.7 

1320 

32 

35.364 

29980 

70 

233.09 

5040 

108 

1004.4 

1278 

33 

37.416 

28420 

71 

243.39 

:  4839 

109 

1039.1 

1248 

34 

39.571 

26940 

72 

254.07 

4648 

110 

1074.7 

1209 

35 

41.833 

25560 

73 

265.14 

4465 

111 

1111.4 

1162 

36 

44.207 

24250 

74 

276.62 

4291 

112 

1149.1 

1126 

37 

46.697 

23020 

75 

288.51 

4124 

113 

1187.9 

1091 

1  These  values  are  taken  from  Peabody's  Steam-Tables. 


MECHANICAL  EQUIVALENT  OF  HEAT. 

l  kilogram-calorie  (1  kilogram  water  raised  1°  C.  at  15°  C.)  =  427.3  kilogrammeters  (at 
sea-level,  latitude  45°,  g  =  980.6  c.  g.  s.). 

1  British  thermal  unit  (l  pound  water  raised  1°  F.  at  59°  F.)  =  778.8  foot  pounds  at  sea- 
level,  latitude  45°. 

1  gram-calorie  (1  gram  of  water  raised  1°  C.  at  15°  C.)  =  4.190  X  107  ergs. 

l  Joule  =  107  ergs. 

=  0.2387  gram-calorie. 


REC'D  LD 

DEC  2  9  1961 


f£B     4   1933 


24Mar'6lCK 


